minimax control of nonlinear evolution equations in this paper we study nonlinear parametric optimal control problems we formulate the relevant minimax problem and prove the existence of an optimal control also we derive necessary conditions for saddle point optimality we also associate to the original optimization problem a dual problem and then for the pair we prove a complete duality theorem finally we present two examples of parabolic distributed parameter systems which illustrate the abstract results

sufficient second order optimality conditions for semilinear control problems with pointwise state constraints second order sufficient optimality conditions are established for the optimal control of semilinear elliptic and parabolic equations with pointwise constraints on the control and the state in contrast to former publications on this subject the cone of critical directions is the smallest possible in the sense that the second order sufficient conditions are the closest to the associated necessary ones the theory is developed for elliptic distributed controls in domains up to dimension three moreover problems of elliptic boundary control and parabolic distributed control are discussed in spatial domains of dimension two and one respectively

second order analysis for optimal control problems improving results expected from abstract theory an abstract optimization problem of minimizing a functional on a convex subset of a banach space is considered we discuss natural assumptions on the functional that permit establishing sufficient second order optimality conditions with minimal gap with respect to the associated necessary ones though the two norm discrepancy is taken into account the obtained results exhibit the same formulation as the classical ones known from finite dimensional optimization we demonstrate that these assumptions are fulfilled in particular by important optimal control problems for partial differential equations we prove that in contrast to a widespread common belief the standard second order conditions formulated for these control problems imply strict local optimality of the controls not only in the sense of l infty but also of l 2

minimax control of nonlinear evolution equations in this paper we study nonlinear parametric optimal control problems we formulate the relevant minimax problem and prove the existence of an optimal control also we derive necessary conditions for saddle point optimality we also associate to the original optimization problem a dual problem and then for the pair we prove a complete duality theorem finally we present two examples of parabolic distributed parameter systems which illustrate the abstract results

sufficient second order optimality conditions for a parabolic optimal control problem with pointwise control state constraints an optimal control problem for a semilinear parabolic equation is investigated where pointwise constraints are given on the control and the state the state constraints are of mixed bottleneck type where associated lagrange multipliers can be assumed to be bounded and measurable functions based on this property a second order sufficient optimality condition is established that considers strongly active constraints

a priori error estimates for space time finite element discretization of semilinear parabolic optimal control problems in this paper a priori error estimates for space time finite element discretizations of optimal control problems governed by semilinear parabolic pdes and subject to pointwise control constraints are derived we extend the approach from meidner and vexler siam control optim 47 3 1150 1177 2008 siam control optim 47 3 1301 1329 2008 where linear quadratic problems have been considered discretizing the state equation by usual conforming finite elements in space and a discontinuous galerkin method in time error estimates for controls discretized by piecewise constant functions in time and cellwise constant functions in space are derived in detail and we explain how error estimate for further discretization approaches e g cellwise linear discretization in space the postprocessing approach from meyer and rosch siam j control optim 43 970 985 2004 and the variationally discrete approach from hinze j comput optim appl 30 45 63 2005 can be obtained in addition we derive an estimate for a setting with finitely many time dependent controls

a fixed mesh method for incompressible flow structure systems with finite solid deformations a fixed mesh algorithm is proposed for simulating flow structure interactions such as those occurring in biological systems in which both the fluid and solid are incompressible and the solid deformations are large several of the well known difficulties in simulating such flow structure interactions are avoided by formulating a single set of equations of motion on a fixed eulerian mesh the solid s deformation is tracked to compute elastic stresses by an overlapping lagrangian mesh in this way the flow structure interaction is formulated as a distributed body force and singular surface force acting on an otherwise purely fluid system these forces which depend on the solid elastic stress distribution are computed on the lagrangian mesh by a standard finite element method and then transferred to the fixed eulerian mesh where the joint momentum and continuity equations are solved by a finite difference method the constitutive model for the solid can be quite general for the force transfer standard immersed boundary and immersed interface methods can be used and are demonstrated we have also developed and demonstrated a new projection method that unifies the transfer of the surface and body forces in a way that exactly conserves momentum the interface is still effectively sharp for this approach the spatial convergence of the method is observed to be between first and second order as in most immersed boundary methods for membrane flows the algorithm is demonstrated by the simulations of an advected elastic disk a flexible leaflet in an oscillating flow and a model of a swimming jellyfish

existence uniqueness and behavior of solutions for a class of nonlinear parabolic problems abstract we prove existence uniqueness regularity results and estimates describing the behavior both for large and small times of a solution u of some nonlinear parabolic equations of leray lions type including the p laplacian in particular we show how the summability of the initial datum u 0 and the value of p influence the behavior of the solution u producing ultracontractive or supercontractive estimates or extinction in finite time or different kinds of decay estimates

numerical simulation of air pollution due to traffic flow in urban networks abstract as it is well known traffic flow is the main pollution source in many urban areas where the number of vehicles ranges from many thousands to millions thus estimating the pollution emission rate due to traffic flow in big cities is a very hard task to approach this environmental issue in this paper we propose a methodology that consists of combining the 1d lighthill whitham richards traffic model for road networks with a classical 2d advection diffusion reaction pollution model for the atmosphere here the pollution model uses a source term that takes into account the traffic flow contamination by means of a radon measure supported on a road network within an urban domain furthermore we establish the existence of solution of the coupled model and detail a complete numerical algorithm to compute it mainly interfacing a finite volume scheme based on the supply demand method for the traffic model with a characteristics lagrange finite element method for the pollution model finally several numerical experiences for a real urban domain the guadalajara metropolitan area in mexico are presented

parabolic control problems in measure spaces with sparse solutions optimal control problems in measure spaces lead to controls that have small support which is desirable e g in the context of optimal actuator placement for problems governed by parabolic partial differential equations well posedness is guaranteed in the space of square integrable measure valued functions which leads to controls with a spatial sparsity structure a conforming approximation framework allows one to derive numerically accessible optimality conditions as well as convergence rates in particular although the state is discretized the control problem can still be formulated and solved in the measure space numerical examples illustrate the structural features of the optimal controls

a non overlapping domain decomposition method with non matching grids for modeling large finite antenna arrays a non overlapping domain decomposition method ddm is proposed herein to solve maxwell equations in r 3 in this work the maxwell equations are discretized using a vector finite element method with hierarchical h curl vector basis functions there are two major ingredients in the proposed non overlapping ddm a a proper 1st order transmission condition to enforce field continuity across domain boundaries and b a cement technique to allow non matching grids for neighboring domains moreover a detail fourier analysis of the transmission condition for a canonical half space example is presented the analysis provides significant insights into the convergence behavior of the proposed non overlapping ddm for solving electromagnetic radiation problems such as the large finite antenna arrays particularly for the antenna arrays the proposed non overlapping ddm is extremely efficient since the formulation can easily incorporate geometrical repetitions exponentially tapered notch vivaldi antenna arrays with size up to 100x100 elements are solved on a common pc to validate the proposed non overlapping ddm

necessary optimality conditions for control problems and the stone cech compactification this paper deals with optimal control problems of parabolic equations in the presence of pointwise state constraints we consider bounded controls which act in the initial condition of the state equation the state variable is a bounded continuous function on the domain q omega times 0 t but is not continuous on overline q in this case the multiplier associated with state constraints is a regular bounded finitely additive measure on q but not a sigma additive one using some properties of the stone u c ech compactification we prove a decomposition theorem for this measure which allows us to interpret the adjoint equation in a classical sense we obtain new optimality conditions for these kinds of problems and we apply these results to the case of bilateral constraints

conservative load transfer along curved fluid solid interface with non matching meshes we investigate the effect of curvature on the accuracy of schemes used to transfer loads along the interface in coupled fluid solid simulations involving non matching meshes we analyze two types of load transfer schemes for the coupled system a point to element projection schemes and b common refinement schemes the accuracy of these schemes over the curved interface is assessed with the aid of static and transient problems we show that the point to element projection schemes may yield inaccurate load transfer from the source fluid mesh to the target solid mesh leading to a weak instability in the form of spurious oscillations and overshoots in the interface solution the common refinement scheme resolves this problem by providing an accurate transfer of discrete interface conditions across non matching meshes we show theoretically that the accurate transfer preserves the stability of the coupled system while maintaining the energy conservation over a reference interface finally we introduce simple analytical error functions which correlate well with the numerical errors of the load transfer schemes

non conforming curved finite element schemes for time dependent elastic acoustic coupled problems high order numerical methods for solving time dependent acoustic elastic coupled problems are introduced these methods based on finite element techniques allow for a flexible coupling between the fluid and the solid domain by using non conforming meshes and curved elements since characteristic waves travel at different speeds through different media specific levels of granularity for the mesh discretization are required on each domain making impractical a possible conforming coupling in between advantageously physical domains may be independently discretized in our framework due to the non conforming feature consequently an important increase in computational efficiency may be achieved compared to other implementations based on conforming techniques namely by reducing the total number of degrees of freedom differently from other non conforming approaches proposed so far our technique is relatively simpler and requires only a geometrical adjustment at the coupling interface at a preprocessing stage so that no extra computations are necessary during the time evolution of the simulation on the other hand as an advantage of using curvilinear elements the geometry of the coupling interface between the two media of interest is faithfully represented up to the order of the scheme used in other words higher order schemes are in consonance with higher order approximations of the geometry concerning the time discretization we analyze both explicit and implicit schemes these schemes are energy conserving and for the explicit case the stability is guaranteed by a cfl condition in order to illustrate the accuracy and convergence of these methods a set of representative numerical tests are presented

combined interface boundary condition method for fluid rigid body interaction abstract this research is motivated by the recent work which has presented a new loosely coupled partitioned algorithm for fluid structure interaction fsi r jaiman p geubelle e loth x jiao combined interface boundary condition method for unsteady fluid structure interaction comput methods appl mech engrg 200 2011 27 39 the loosely coupled partitioned algorithm is intrinsically exposed to the notorious time lag effect whose remedy promotes the combined interface boundary condition cibc method in this method correction terms for velocity and traction are introduced at two sequential time steps with a coupling parameter that plays an important part in the stability and accuracy of the coupled system the structural traction ratio that appears explicitly in the traction correction is estimated based on the solution of the structural subsystem this handling asks for the structural traction before it is corrected by the cibc method in this paper a new formulation for the cibc method is developed to repair the aforementioned inconvenience after simple manipulation the structural traction ratio is removed in constructing the traction correction therefore the structural traction is no more needed in cibc correction terms meantime the ratio t is employed to tune the interfacial corrections instead of the coupling parameter an arbitrary lagrangian eulerian finite element method is used to analyze fsi the characteristic based split cbs scheme is employed to solve incompressible navier stokes equations while the equation for rigid body dynamics is solved by newmark method a numerical technique called moving submesh approach is performed for the mesh deformation for respecting geometric conservation law a mass source term is implanted into the cbs scheme on the moving mesh several numerical examples are tested to validate the proposed methodology for fluid rigid body interaction the obtained results are in agreement with the existing data and some famous features of flow phenomena have been detected successfully

second order and stability analysis for optimal sparse control of the fitzhugh nagumo equation optimal sparse control problems are considered for the fitzhugh nagumo system including the so called schlogl model the nondifferentiable objective functional of tracking type includes a quadratic tikhonov regularization term and the l 1 norm of the control that accounts for the sparsity though the objective functional is not differentiable a theory of second order sufficient optimality conditions is established for tikhonov regularization parameter nu 0 and also for the case nu 0 in this context also local minima are discussed that are strong in the sense of the calculus of variations the second order conditions are used as the main assumption for proving the stability of locally optimal solutions with respect to nu to 0 and with respect to perturbations of the desired state functions the theory is confirmed by numerical examples that are resolved with high precision to confirm that the optimal solution obeys the system of necessary optimality conditions

overlapping nonmatching grid mortar element methods for elliptic problems in the first part of the paper we introduce an overlapping mortar finite element method for solving two dimensional elliptic problems discretized on overlapping nonmatching grids we prove an optimal error bound and estimate the condition numbers of certain overlapping schwarz preconditioned systems for the two subdomain case we show that the error bound is independent of the size of the overlap and the ratio of the mesh parameters in the second part we introduce three additive schwarz preconditioned conjugate gradient algorithms based on the trivial and harmonic extensions we provide estimates for the spectral bounds on the condition numbers of the preconditioned operators we show that although the error bound is independent of the size of the overlap the condition number does depend on it numerical examples are presented to support our theory

brief control of nonlinear distributed parameter systems using generalized invariants a framework is presented to facilitate the formulation of control strategies for nonlinear dps the key contribution is the generalized quantitative expression of the stability condition for any nonlinear dps the methodology derives from the use of symmetry groups that determine the group invariant solutions of a differential system an invariance condition in the prolonged space of the differential system provides the framework for the distributed control law

on the lagrange newton sqp method for the optimal control of semilinear parabolic equations a class of lagrange newton sqp methods is investigated for optimal control problems governed by semilinear parabolic initial boundary value problems distributed and boundary controls are given restricted by pointwise upper and lower bounds the convergence of the method is discussed in appropriate banach spaces based on a weak second order sufficient optimality condition for the reference solution local quadratic convergence is proved the proof is based on the theory of newton methods for generalized equations in banach spaces

non linear elliptic and parabolic equations involving measure data in this paper we prove the existence of solutions for equations of the type div a du f in a bounded open set u 0 on where a is a possibly non linear function satisfying some coerciveness and monotonicity assumptions and f is a bounded measure we also consider the equation div a du g u f in u 0 on with f l1 or f m u u 0 and the parabolic equivalent of the first elliptic equation

karush kuhn tucker conditions for nonsmooth mathematical programming problems in function spaces lagrange multiplier rules for abstract optimization problems with mixed smooth and convex terms in the cost with smooth equality constrained and convex inequality constraints are presented the typical case for the equality constraints that the theory is meant for is given by differential equations applications are given to l 1 minimum norm control problems l infty norm minimization and a class of optimal control problems with distributed state constraints and nonsmooth cost

second order analysis for strong solutions in the optimal control of parabolic equations in this paper we provide a second order analysis for strong solutions in the optimal control of parabolic equations we consider the case of box constraints on the control and final integral constraints on the state in contrast to sufficient conditions assuring quadratic growth in the weak sense i e when the cost increases at least quadratically for admissible controls uniformly near to the nominal one see e g 16 26 our main result provides a sufficient condition for quadratic growth of the cost for admissible controls whose associated states are uniformly near to the state of the nominal one as a consequence of our results for qualified problems with a strictly convex and quadratic hamiltonian we prove that both notions of quadratic growth coincide

a new three dimensional variable node finite element and its application for fluid solid interaction problems abstract a new three dimensional variable node element is proposed to achieve an efficient connection of non matching interfaces between dissimilar finite element meshes the variable node elements at interfaces are compatible with conventional finite elements and satisfy the interface conditions of continuity and completeness across non matching meshes the present method thereby provides a seamless connection between dissimilar finite element meshes and a correct load transfer across non matching interfaces therefore it leads to an efficient approach for solving a class of problems involving the non matching interfaces such as fluid solid interaction problems numerical examples are presented to show the effectiveness of the present method for solving fluid solid interaction problems with non conforming interfaces and the usefulness and application of the present method are discussed

necessary optimality conditions for infinite dimensional state constrained control problems abstract this paper is concerned with first order necessary optimality conditions for state constrained control problems in separable banach spaces assuming inward pointing conditions on the constraint we give a simple proof of pontryagin maximum principle relying on infinite dimensional neighboring feasible trajectories theorems proved in 20 further we provide sufficient conditions guaranteeing normality of the maximum principle we work in the abstract semigroup setting but nevertheless we apply our results to several concrete models involving controlled pdes pointwise state constraints as positivity of the solutions are allowed

pontryagin s maximum principle of optimal control governed by some non well posed semilinear parabolic differential equations this paper concerns about necessary conditions for optimal control problems governed by some semilinear parabolic differential equations which may be non well posed the two point boundary time variable state constraint involves the control set may be non convex

optimal boundary control of hyperbolic equations with pointwise state constraints in this paper we consider dynamic optimization problems for hyperbolic systems with boundary controls and pointwise state constraints in contrast to parabolic dynamics such systems have not been sufficiently studied in the literature the reason is the lack of regularity in the case of hyperbolic dynamics we present necessary optimality conditions for both neumann and dirichlet boundary control problems and discuss differences and relationships between them

the completion of the manifold of riemannian metrics we give a description of the completion of the manifold of all smooth riemannian metrics on a fixed smooth closed finite dimensional orientable manifold with respect to a natural metric called the l metric the primary motivation for studying this problem comes from teichmuller theory where similar considerations lead to a completion of the well known weil petersson metric we give an application of the main theorem to the completions of teichmuller space with respect to a class of metrics that generalize the weil petersson metric

neumann boundary control of hyperbolic equations with pointwise state constraints we consider optimal control problems for hyperbolic equations with controls in neumann boundary conditions with pointwise constraints on the control and state functions focusing on the multidimensional wave equation with a nonlinear term we derive new necessary optimality conditions in the form of a pointwise pontryagin maximum principle for the state constrained problem under consideration our approach is based on modern methods of variational analysis that allow us to obtain refined necessary optimality conditions with no convexity assumptions on integrands in the minimizing cost functional

adaptive finite element method for parabolic equations with dirac measure abstract in this paper we study the adaptive finite element method for parabolic equations with dirac measure two kinds of problems with separate measure data in time and measure data in space are considered it is well known that the solutions of such kind of problems may exhibit lower regularity due to the existence of the dirac measure and thus fit to adaptive fem for space discretization and variable time steps for time discretization for both cases we use piecewise linear and continuous finite elements for the space discretization and backward euler scheme or equivalently piecewise constant discontinuous galerkin method for the time discretization the a posteriori error estimates based on energy and l 2 norms for the fully discrete problems are then derived to guide the adaptive procedure numerical results are provided at the end of the paper to support our theoretical findings

optimal control of semilinear parabolic equations by bv functions optimal control problems for semilinear parabolic equations with control costs involving the total bounded variation seminorm are analyzed this choice of control cost favors optimal controls which are piecewise constant and it penalizes the number of jumps it is an appropriate choice if a simple structure of the optimal controls is desired which however is still sufficiently flexible so that good tracking properties can be maintained existence of optimal controls necessary and sufficient optimality conditions and sparsity properties of the derivatives are obtained convergence of a finite element approximation is analyzed and numerical examples illustrating structural properties of the optimal controls are provided

a hybrid multi time step framework for pore scale and continuum scale modeling of solute transport in porous media abstract in this paper we propose a computational framework which is based on a domain decomposition technique to employ both finite element method which is a popular continuum modeling approach and lattice boltzmann method which is a popular pore scale modeling approach in the same computational domain to bridge the gap across the disparate length and time scales we first propose a new method to enforce continuum scale boundary conditions i e dirichlet and neumann boundary conditions onto the numerical solution from the lattice boltzmann method this method is based on maximization of entropy and preserve the non negativity of discrete distributions under the lattice boltzmann method the proposed computational framework allows different grid sizes orders of interpolation and time steps in different subdomains this allows for different desired resolutions in the numerical solution in different subdomains through numerical experiments the effect of grid and time step refinement disparity of time steps in different subdomains domain partitioning and the number of iteration steps on the accuracy and rate of convergence of the proposed methodology are studied finally to showcase the performance of this framework in porous media applications we use it to simulate the dissolution of calcium carbonate in a porous structure

identification of space time distributed parameters in the gierer meinhardt reaction diffusion system we consider parameter identification for the classic gierer meinhardt reaction diffusion system the original gierer meinhardt model a gierer and h meinhardt kybernetik 12 1972 pp 30 39 was formulated with constant parameters and has been used as a prototype system for investigating pattern formation in developmental biology in our paper the parameters are extended in time and space and used as distributed control variables the methodology employs pde constrained optimization in the context of image driven spatiotemporal pattern formation we prove the existence of optimal solutions derive an optimality system and determine optimal solutions the results of numerical experiments in two dimensions are presented using the finite element method which illustrates the convergence of a variable step gradient algorithm for finding the optimal parameters of the system a practical target function is constructed for the optimal control algorithm corresponding to the actual image of a marine angel

optimal management of an urban road network with an environmental perspective abstract within the framework of numerical simulation and optimal control of partial differential equations in this work we deal with the mathematical modelling and optimal management of urban road networks in particular we are interested in finding the optimal management of the network intersections in order to reduce traffic congestion and atmospheric pollution so we consider two different multi objective control problems the former from a cooperative viewpoint the latter within a hierarchical paradigm propose a complete numerical algorithm to solve them and finally present several numerical tests for a realistic case posed in the guadalajara metropolitan area mexico where the possibilities of our methodology are shown

spike controls for elliptic and parabolic pdes abstract we analyze the use of measures of the minimal norm to control elliptic and parabolic equations we prove the sparsity of the optimal control in the parabolic case we prove that the solution of the optimization problem is a borel measure supported in a set of lebesgue measure zero in both cases the approximate controllability can be achieved efficiently by means of controls that are activated in some finite number of pointwise locations we also analyze the corresponding dual problem

a stable second order partitioned iterative scheme for freely vibrating low mass bluff bodies in a uniform flow abstract we present a stable partitioned iterative scheme for solving fluid body interaction problems at low structure to fluid mass ratio the scheme relies on the so called nonlinear interface force correction based on aitken s extrapolation process to stabilize the coupled partitioned system employing an arbitrary lagrangian eulerian finite element framework approximate interface force correction is constructed through subiterations to account for the missing effects of off diagonal jacobian terms in the partitioned staggered scheme through the generalized aitken s geometric extrapolation process with a dynamic stabilization parameter the interface corrections allow to satisfy the force equilibrium with arbitrary accuracy while expanding the scope of partitioned iterative schemes for fluid structure interaction with strong added mass effects to assess the proposed iterative scheme against the standard strong coupling effects of mass ratio are investigated for a freely vibrating circular cylinder we show that our second order scheme is stable for low mass density ratio and hence is able to handle strong added mass effects the numerical stability and robustness of the scheme is then demonstrated for a new application of tandem square cylinder undergoing complex wake induced vibration and galloping

a priori error analysis for finite element approximation of parabolic optimal control problems with pointwise control we consider finite element approximations of parabolic control problems with pointwise control the state equation exhibits low regularity due to the control imposed pointwisely this introduces some difficulties for both theoretical and numerical analysis to discretize the optimal control problem we use variational discretization together with piecewise linear and continuous finite elements for the space discretization of the state and we use the backward euler scheme for time discretization we prove a priori error estimates for the control state and adjoint state numerical experiments are provided which support the theoretical results

state constrained optimal control problems with states of low regularity we consider first order optimality conditions for state constrained optimal control problems in particular we study the case where the state equation does not have enough regularity to admit existence of a slater point in function space we overcome this difficulty by a special transformation under a density condition we show existence of lagrange multipliers which have a representation via measures and additional regularity properties

maximum principle for a hybrid system via singular perturbations we prove a maximum principle of pontryagin type for the time optimal control of a hybrid system the system is nonlinear and consists of a controlled coupled ode pde the control input acts via the boundary and the interior of the domain systems of this type frequently arise in modeling population dynamics in a contaminated environment for the regularization we use ekeland s variational principle along with a singular perturbation technique for this purpose we introduce a new trajectory on an additional exterior domain whose size may be considered as a singular perturbation parameter it turns out that the maximum principle is stable with respect to the size of the additional exterior domain the technique allows us to obtain necessary optimality conditions without involving measure boundary data

first and second order optimality conditions for a class of optimal control problems with quasilinear elliptic equations a class of optimal control problems for quasilinear elliptic equations is considered where the coefficients of the elliptic differential operator depend on the state function first and second order optimality conditions are discussed for an associated control constrained optimal control problem main emphasis is laid on second order sufficient optimality conditions to this aim the regularity of the solutions to the state equation and its linearization is studied in detail and the pontryagin maximum principle is derived one of the main difficulties is the nonmonotone character of the state equation

on the structure of lagrange multipliers for state constrained optimal control problems abstract state constrained optimal control problems represent severe analytical and numerical challenges it is shown that under certain conditions on the active set the measure representing the lagrange multiplier associated to the state constraint can be decomposed in a distributed part in l2 with support on the active set and a boundary measure concentrated on the interface between active and inactive sets

ricci flow and the metric completion of the space of kahler metrics we consider the space of kahler metrics as a riemannian submanifold of the space of riemannian metrics and study the associated submanifold geometry in particular we show that the intrinsic and extrinsic distance functions are equivalent we also determine the metric completion of the space of kahler metrics making contact with recent generalizations of the calabi yau theorem due to dinew and guedj zeriahi as an application we obtain a new analytic stability criterion for the existence of a kahler einstein metric on a fano manifold in terms of the ricci flow and the distance function we also prove that the kahler ricci flow converges as soon as it converges in the metric sense

on regularity of solutions and lagrange multipliers of optimal control problems for semilinear equations with mixed pointwise control state constraints a class of nonlinear elliptic and parabolic optimal control problems with mixed control state constraints is considered extending a method known for the control of ordinary differential equations to the case of pdes the yosida hewitt theorem is applied to show that the lagrange multipliers are functions of certain l p spaces by bootstrapping arguments under natural assumptions optimal controls are shown to be lipschitz continuous in the elliptic case and holder continuous for parabolic problems

pontryagin s principle for state constrained control problems governed by parabolic equations with unbounded controls this paper deals with optimal control problems governed by semilinear parabolic equations with pointwise state constraints and unbounded controls under some strong stability assumption we obtain necessary optimality conditions in the form of a pontryagin s minimum principle in qualified form a pontryagin s principle in nonqualified form is also proved without any stability condition

control of an elliptic problem with pointwise state constraints this paper deals with a quadratic control problem for elliptic equations with pointwise state constraints existence and uniqueness of the solution is proved optimality conditions are given and regularity of the optimal solution is investigated

solvability of a parabolic problem with non smooth data abstract we study a weak solvability of one linear parabolic problem with a summable right hand side and non smooth coefficients we consider this problem as appropriate operator equation in some banach space methods of the semigroups theory fractional powers of operators and integral operators for solvability of this operator equation are used

theoretical and numerical analysis of an optimal control problem related to wastewater treatment in this work we deal with the design and management of wastewater treatment systems mainly the disposal of sea outfalls discharging polluting effluent from a sewerage system this problem is formulated as a pointwise optimal control problem with state and control constraints the main difficulties arise from the lack of regularity of the second member in the state system and from the pointwise constraints on the state variables we develop the theoretical analysis of the problem we propose an algorithm for its numerical resolution and finally we give results for a realistic problem posed in the ria of vigo spain

geodesics distance and the cat 0 property for the manifold of riemannian metrics given a fixed closed manifold m we exhibit an explicit formula for the distance function of the canonical l 2 riemannian metric on the manifold of all smooth riemannian metrics on m additionally we examine the metric completion of the manifold of metrics with respect to the l 2 metric and show that there exists a unique minimal path between any two points this path is also given explicitly as an application of these formulas we show that the metric completion of the manifold of metrics is a cat 0 space

finite element approximations of parabolic optimal control problems with controls acting on a lower dimensional manifold this paper is devoted to the study of finite element approximations to parabolic optimal control problems with controls acting on a lower dimensional manifold the manifold can be a point a curve or a surface which may be independent of time or evolve in the time horizon and is assumed to be strictly contained in the space domain at first we obtain the first order optimality conditions for the control problems and the corresponding regularity results then for the control problems we consider the fully discrete finite element approximations based on the piecewise constant discontinuous galerkin scheme for time discretization and piecewise linear finite elements for space discretization and variational discretization to the control variable a priori error estimates are finally obtained for the fully discretized control problems and supported by numerical examples

a new dual mortar method for curved interfaces 2d elasticity dual mortar method formulations have shown to be a very effective and efficient way for interfacing e g tying contacting dissimilar meshes on the other hand we have recently found that they can sometimes perform quite poorly when applied to curved surfaces in some solid mechanics applications a new modified two dimensional dual mortar method for piecewise linear finite elements is developed that overcomes this deficiency and is demonstrated on a model problem furthermore mathematical analysis is provided to demonstrate the optimal convergence and stability of the new method copyright 2005 john wiley sons ltd

pontryagin maximum principle for semilinear and quasilinearparabolic equations with pointwise state constraints this paper studies the first order necessary conditions for the optimal controls of semilinear and quasilinear parabolic partial differential equations with pointwise state constraints a pontryagin type maximum principle is obtained

a priori error estimates for finite element discretizations of parabolic optimization problems with pointwise state constraints in time in this paper we consider an optimal control problem which is governed by a linear parabolic equation and is subject to state constraints pointwise in time optimal order error estimates are developed for a space time finite element discretization of this problem numerical examples confirm the theoretical results as a by product of our analysis we derive a new regularity result for the optimal control

an extension of pontryagin s principle for state constrained optimal control of semilinear elliptic equations and variational inequalities this paper deals with state constrained optimal control problems governed by semilinear elliptic equations or variational inequalities by using ekeland s principle a minimum principle of pontryagin s type under some stability conditions of the optimal cost with respect to the state constraints is derived

implicit taylor methods for parabolic problems with nonsmooth data and applications to optimal heat control as a rule parabolic problems with nonsmooth data show rapid changes of its solution or even possess solutions of reduced smoothness while for smooth data various time integration methods e g the trapezoidal rule or the euler backwards scheme work efficiently but in case of jumps effects of high frequency oscillations are observable over a long time horizon or steep changes are smeared out implicit taylor methods itm which are mostly applied in specific applications like interval methods but not commonly used for general cases combine high accuracy with strong damping of unwanted oscillations these properties make them a good choice in case of nonsmooth data in the present paper itm are investigated in detail for semi discrete linear parabolic problems in itm at each time level a large scale linear system has to be solved and preconditioned conjugate gradient methods pcg can efficiently be applied here adapted preconditioners are constructed and tight spectral bounds are derived which are independent of the discretization parameters of the parabolic problem as an important application itm are considered in case of boundary heat control occurring control constraints are involved by means of penalty functions to solve the completely discretized problem gradient based numerical algorithms are used where the gradient of the objective is partially evaluated via discrete adjoints and partially by explicitly available terms corresponding to the penalties some test examples illustrate the efficiency of the considered algorithms

a pontryagin maximum principle for infinite dimensional problems a basic idea of the classical approach for obtaining necessary optimality conditions in optimal control is to construct suitable needle like control variations we use this idea to prove the main result of the present paper a pontryagin maximum principle for infinite dimensional optimal control problems with pointwise terminal constraints in arbitrary banach state space by refining the classical variational technique we are able to replace the differentiability of the norm of the state space guaranteed by the strict convexity of its dual norm which is assumed in the known results by a separation argument we also drop another key assumption which is common in the existing literature on infinite dimensional control problems that the set of variations in the state space of the state trajectory s endpoint resulting from the control variations be finite codimensional instead we require only that it has nonempty interior in its closed affine hull as an application of the abstract result we present an illustrative example an optimal control problem for an age structured system with pointwise terminal state constraints

analysis of finite element methods and domain decomposition algorithms for a fluid solid interaction problem this paper is concerned with the finite element galerkin approximations for a fluid solid interaction model proposed in x feng p lee and y wei appl anal submitted both continuous time and discrete time approximations are formulated and analyzed optimal order a priori estimates for the errors in l infty h 1 and l infty l 2 are derived the main difficulty for the error estimates is caused by the interface conditions which describe the interaction between a fluid and a solid on their contact surface and it is overcome by using a boundary duality argument of douglas and dupont numer math 20 1973 pp 213 237 to handle the terms involving the interface conditions parallelizable domain decomposition algorithms are also proposed and analyzed for efficiently solving the finite element systems

optimal control problems for semilinear non well posed parabolic differential equations this paper deals with necessary conditions for optimal control problem governed by some semilinear parabolic differential equation which may be non well posed state constrained problem is considered finally under some suitable assumptions we obtain the existence of optimal pairs

boundary feedback stabilization of the schlogl system the schlogl system is governed by a nonlinear reaction diffusion partial differential equation with a cubic nonlinearity that determines three constant equilibrium states it is a classical example of a chemical reaction system that is bistable the constant equilibrium that is enclosed by the other two constant equilibrium points is unstable in this paper robin boundary feedback laws are presented that stabilize the system in a given stationary state or more generally in a given time dependent desired system orbit the exponential stability of the closed loop system with respect to the l 2 norm is proved in particular it is shown that with the boundary feedback law the unstable constant equilibrium point can be stabilized

optimal control of a parabolic equation with time dependent state constraints in this paper we study the optimal control problem of the heat equation with a cubic nonlinearity by a distributed control over a subset of the domain in the presence of a state constraint the latter is integral over the space and has to be satisfied each time using for the first time the technique of alternative optimality systems in the context of optimal control of partial differential equations we show that both the control and multiplier are continuous in time under some natural geometric hypotheses we can prove that extended polyhedricity holds allowing us to obtain no gap second order optimality conditions that characterize quadratic growth an expansion of the value function and of approximate solutions can be computed for a directional perturbation of the right hand side of the state equation

optimality conditions for stochastic boundary control problems governed by semilinear parabolic equations abstract we study the boundary control problems for stochastic parabolic equations with neumann boundary conditions imposing super parabolic conditions we establish the existence and uniqueness of the solution of state and adjoint equations with non homogeneous boundary conditions by the galerkin approximations method we also find that in this case the adjoint equation bspde has two boundary conditions one is non homogeneous the other is homogeneous by these results we derive necessary optimality conditions for the control systems under convex state constraints by the convex perturbation method

pontryagin s principle for state constrained boundary control problems of semilinear parabolic equations this paper deals with state constrained optimal control problems governed by semilinear parabolic equations we establish a minimum principle of pontryagin s type to deal with the state constraints we introduce a penalty problem by using ekeland s principle the key tool for the proof is the use of a special kind of spike perturbations distributed in the domain where the controls are defined conditions for normality of optimality conditions are given

state constrained optimal control problems governed by coupled nonlinear wave equations with memory this work considers the optimal control problems governed by coupled nonlinear wave equations with memory where the state constraint is a type of integral first we investigate the existence of the optimal solution for the optimal control problem and then we deduce the maximum principle for the optimal solution with state constraint moreover we give a concrete example which is covered by the main result

global attractors for the p laplacian equations with nonregular data abstract let be a smooth bounded domain in r n n 3 we consider the long time behavior of solutions to the p laplacian equation u t p u f u g where 2 p n p div u p 2 u is the p laplace operator assume that g and the initial condition u 0 lie in l 1 f r r is of class c 1 and satisfies proper growth conditions firstly we prove the uniqueness of the entropy solution and establish some regularity results then we show the existence of a global attractor a in l r 1 w 0 1 s with s max n p 1 n 1 p r 1 r to obtain the results a decomposition method and a bootstrap technique are used

explicit synchronous partitioned algorithms for interface problems based on lagrange multipliers abstract traditional explicit partitioned schemes exchange boundary conditions between subdomains and can be related to iterative solution methods for the coupled problem as a result these schemes may require multiple subdomain solves acceleration techniques or optimized transmission conditions to achieve sufficient accuracy and or stability we present a new synchronous partitioned method derived from a well posed mixed finite element formulation of the coupled problem we transform the resulting differential algebraic equation dae to a hessenberg index 1 form in which the algebraic equation defines the lagrange multiplier as an implicit function of the states using this fact we eliminate the multiplier and reduce the dae to a system of explicit odes for the states explicit time integration both discretizes this system in time and decouples its equations as a result the temporal accuracy and stability of our formulation are governed solely by the accuracy and stability of the explicit scheme employed and are not subject to additional stability considerations as in traditional partitioned schemes we establish sufficient conditions for the formulation to be well posed and prove that classical mortar finite elements on the interface are a stable choice for the lagrange multiplier we show that in this case the condition number of the schur complement involved in the elimination of the multiplier is bounded by a constant the paper concludes with numerical examples illustrating the approach for two different interface problems

second order necessary and sufficient optimality conditions for optimization problems and applications to control theory this paper deals with a class of nonlinear optimization problems in a function space where the solution is restricted by pointwise upper and lower bounds and by finitely many equality and inequality constraints of functional type second order necessary and sufficient optimality conditions are established where the cone of critical directions is arbitrarily close to the form which is expected from the optimization in finite dimensional spaces the results are applied to some optimal control problems for ordinary and partial differential equations

optimal control of semilinear parabolic equations with k approximate periodic solutions in this paper we study some optimal control problems governed by certain semilinear parabolic equations with mathcal k approximate periodic solutions we first prove the existence and uniqueness theorems for mathcal k approximate periodic solutions of the equations we then use these results to establish the qualified pontryagin maximum principle the existence for such optimal controls is also investigated in the paper

a perturbed lagrangian formulation for the finite element solution of contact problems making use of a perturbed lagrangian formulation a finite element procedure for contact problems is developed for the general case in which node to node contact no longer holds the proposed procedure leads naturally to a discretization of the contact interface into contact segments within the context of a bilinear interpolation for the displacement field a mixed finite element approximation is introduced by assuming discont naous contact pressure constant on the contact segment because of this piece wise constant approximation the gap function enters into the formulation in an average sense instead of through a point wise definition numerical examples are presented that illustrate the performance of the proposed procedure current finite element formulations for contact problems based on either the classical lagrange parameter procedure l 3 12 203 or the penalty function method 4 6 11 are characterized by a point wise enforcement of the contact constraint condition in the sense that penetration of the bodies is established on a nodal basis moreover in this methods the recovery of the contact pressure over the element from the contact nodal forces generally requires an additional procedure within the framework of classical lagrange multiplier methods the contact condition is exactly satisfied by transforming the constrained problem into an unconstrained one with the introduction of additional variables lagrange multipliers these extra variables add computational effort to the solution process which often requires special procedures to handle the presence of zero diagonal terms penalty methods on the other hand enable one to transform the constrained problem into an unconstrained one without introducing additional variables the constraint condition is now satisfied only approximately for finite values of the penalty parameter the main difhculty associated with these methods however lies in the poor conditioning of the problem as the penalty is increased to more accurately enforce the constraint condition this is a well understood phenomenon particularly in the context of the incompressible and nearly incompressible problem in solid and fluid mechanics e g see l 22 25 for a review recently augmented lagrangian procedures have been proposed as a promising way to partially overcome these difficulties and regularize the penalty formulation e g see the survey in 7 8 within the framework of zinearited e u c it is possible to restrict the finite element formulation of contact problems by assuming that node to node contact occurs this is in fact the case often considered in the literature l 2 4 6 12 20 211 in the general context of fully

optimal problems for nonlinear parabolic boundary control systems this paper considers optimal problems for boundary control systems with the control acting through a general nonlinear boundary condition the problems include constraints on the control and target conditions the final result is a version of pontryagin s maximum principle this setup covers such physical situations as stefan boltzmannboundary conditions and is based on an abstract theory of nonlinear programming problems

analysis and semidiscrete galerkin approximation of a class of nonlinear parabolic optimal control problems abstract this paper presents an optimization problem involving a system governed by a nonlinear partial differential equation with control acting on the domain in the boundary conditions or in the initial condition we describe the galerkin approximation and prove its convergence to the solutions of the initial optimization problem

optimal control of fluid dynamic systems with state constraint of pointwise type abstract the aim of this work is to obtain the maximum principle by spike perturbation for the optimal control problem with pointwise type state constraint governed by 3 dimensional fluid dynamic systems

conservative load projection and tracking for fluid structure problems the loose coupling of computational fluid dynamics and computational structural dynamics solvers introduces some problems related to the information transfer between the codes some techniques developed to solve the problems of the load transfer and interface surface tracking are presented the main criterion is to achieve conservation of total loads and total energy the load projection scheme is based on gaussian integration and fast interpolation algorithms for unstructured grids the surface tracking algorithm also based on interpolation is important for many applications including aeroelastic deformation of wings due to aerodynamic loads the methodologies not only improve present fluid structure interaction simulations but also increase the range of their applicability these techniques are of general character and can be used in other multidisciplinary applications as well

a variational flexible multibody formulation for partitioned fluid structure interaction application to bat inspired drones and unmanned air vehicles abstract we present a three dimensional 3d partitioned aeroelastic formulation for a flexible multibody system interacting with incompressible turbulent fluid flow while the incompressible navier stokes system is discretized using a stabilized petrov galerkin procedure the multibody structural system consists of a generic interaction of multiple components such as rigid body beams and flexible thin shells along with various types of joints and connections among them a co rotational framework is utilized for the category of small strain problems where the displacement of the body is decomposed into a rigid body rotation and a small strain component this assumption simplifies the structural equations and allows for the incorporation of multiple bodies rigid as well as flexible in the system the displacement and rotation constraints at the joints are imposed by a lagrange multiplier method the equilibrium conditions at the fluid structure interface are satisfied by the transfer of tractions and structural displacements via the radial basis function approach a scattered data interpolation technique which is globally conservative for the coupled stability in low structure to fluid mass ratio regimes a nonlinear iterative force correction scheme is employed in the partitioned staggered predictor corrector scheme the convergence and generality of the radial basis function mapping are analyzed by carrying out systematic error analysis of the transfer of fluid traction across the non matching fluid structure interface where a third order of convergence is observed the proposed aeroelastic framework is then validated by considering a flow across a flexible pitching plate configuration with serration at the trailing edge finally we demonstrate the flow across a flexible flapping wing of a bat modeling the bone fingers as beams and the flexible membrane as thin shells in the multibody system along with the joints

optimal control for semilinear evolutionary variational bilateral problem this paper is concerned with an optimal control problem for some semilinear evolutionary variational inequalities associated with bilateral constraints the control domain is a general separable metric space and has no algebraic structure in particular it is not necessarily convex existence and optimality conditions of optimal pairs are established

boundary control of semilinear elliptic equations with pointwise state constraints this paper is concerned with state constrained optimal control problems of semilinear elliptic equations the control being on the boundary optimality conditions are derived and regularity of the optimal solution is investigated

pontryagin s principle for local solutions of control problems with mixed control state constraints this paper deals with optimal control problems of semilinear parabolic equations with pointwise state constraints and coupled integral state control constraints we obtain necessary optimality conditions in the form of a pontryagin s minimum principle for local solutions in the sense of l p p leq infty