optimal control of obstacle for quasi linear elliptic variational bilateral problems this paper is concerned with an optimal control problem for quasi linear elliptic variational inequality in which the bilateral obstacles are the control the cost functional of this optimal control problem is of lagrange type in which the pth power of laplacian of the control appears this feature leads to the fact that it is hard to derive the optimality system for the underlying problem in this paper the optimality system is established by utilizing the special structure of the approximate optimality system including the monotonicity of the leading differential operator

symmetric positive solutions to singular system with multi point coupled boundary conditions in this paper we study the existence and multiplicity of symmetric positive solutions for a nonlinear system with multi point coupled boundary conditions the arguments are based upon a specially constructed cone and the fixed point index theorem in cones an example is then given to demonstrate the applicability of our results

the multiple reciprocity method applied to thermal stress problems in this paper the multiple reciprocity boundary element method is applied to transform domain integrals due to thermal loadings into equivalent boundary integrals the resulting formulation is restricted to two dimensional elastic and isotropic materials with any steady state temperature distribution including internal heat generation several numerical examples are presented to validate the formulation and demonstrate the accuracy of the method

parabolic systems with coupled boundary conditions we consider elliptic operators with operator valued coefficients and discuss the asso ciated parabolic problems the unknowns are functions with values in a hilbert space w the system is equipped with a general class of coupled boundary conditions of the form f 2 y and f 2 y where y is a closed subspace of l 2 w we discuss well posedness and further qual itative properties systematically reducing features of the parabolic system to operator theoretical properties of the orthogonal projection onto y

optimal control of bilateral obstacle problems we consider an optimal control problem where the state satisfies a bilateral elliptic variational inequality and the control functions are the upper and lower obstacles we seek a state that is close to a desired profile and the h2 norms of the obstacles are not too large existence results are given and an optimality system is derived a particular case is studied that needs no compactness assumption via a monotonicity method

the existence results for obstacle optimal control problems this paper is concerned with the existence of an optimal control problem for a quasi linear elliptic obstacle variational inequality in which the obstacle is taken as the control firstly we get some existence results under the assumption of the leading operator of the variational inequality with a monotone type mapping in section 2 in section 3 as an application without the assumption of the monotone type mapping for the leading operator of the variational inequality we prove that the leading operator of the variational inequality is a monotone type mapping existence of the optimal obstacle is proved the method used here is different from y y zhou x q yang k l teo the existence results for optimal control problems governed by a variational inequality j math anal appl 321 2006 595 608

optimal l p l q estimates for parabolic boundary value problems with inhomogeneous data in this paper we investigate vector valued parabolic initial boundary value problems mathcal a t x d mathcal b j t x d subject to general boundary conditions in domains g in mathbb r n with compact c 2m boundary the top order coefficients of mathcal a are assumed to be continuous we characterize optimal l p l q regularity for the solution of such problems in terms of the data we also prove that the normal ellipticity condition on mathcal a and the lopatinskii shapiro condition on mathcal a mathcal b 1 dots mathcal b m are necessary for these l p l q estimates as a byproduct of the techniques being introduced we obtain new trace and extension results for sobolev spaces of mixed order and a characterization of triebel lizorkin spaces by boundary data

optimal control of the obstacle for a parabolic variational inequality abstract an optimal control problem for a parabolic obstacle variational inequality is considered the obstacle in l2 0 t h2 h10 with t l2 q is taken as the control and the solution to the obstacle problem is taken as the state the goal is to find the optimal control so that the state is close to the desired profile while the norm of the obstacle is not too large existence and necessary conditions for the optimal control are established

parabolic evolution equations and nonlinear boundary conditions on etudie le probleme aux valeurs limites et initiales u 7b a t u f t u 7b b t u g t u 0 t t u 0 u 0 qui peut etre considere comme une contrepartie abstraite a des problemes paraboliques semilineaires

numerical study of an optimal control problem for a catalytic converter function abstract we introduce a model of a catalytic converter and we study mathematical properties of a control function and a cost function as an optimal control problem we give a finite difference scheme for solving various cost functions and discuss the results

modeling and minimization of extinction in volterra lotka type equations with free boundaries abstract an equation of the distributed volterra lotka type with free boundary of the obstacle type with possible applications in ecology when extinction of the biological species is of particular concern is introduced and solved an optimal control problem for such an equation and in particular the problem of minimization of the area of extinction of the species is introduced and to some extent solved

optimal obstacle control problem for semilinear evolutionary bilateral variational inequalities this paper is concerned with an optimal control problem for semilinear evolutionary bilateral variational inequalities the pair of the upper and lower obstacles is taken as the control and the corresponding state is chosen close to a desired target profile with the norms of the obstacles not too large existence and optimality conditions for the problem are derived

the existence results for optimal control problems governed by a variational inequality in this paper we establish the existence of the optimal control for an optimal control problem where the state of the system is defined by a variational inequality problem with monotone type mappings moreover as an application we get several existence results of an optimal control for the optimal control problem where the system is defined by a quasilinear elliptic variational inequality problem with an obstacle

boundary optimal control for nonlinear antiplane problems abstract we consider a nonlinear antiplane problem which models the deformation of an elastic cylindrical body in frictional contact with a rigid foundation the contact is modelled with tresca s law of dry friction in which the friction bound is slip dependent the aim of this article is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target by acting with a control on the boundary of the body the existence of at least one optimal control is proved next we introduce a regularized problem depending on a small parameter and we study the convergence of the optimal controls when tends to zero an optimality condition is delivered for the regularized problem

c stationarity for optimal control of static plasticity with linear kinematic hardening an optimal control problem is considered for the variational inequality representing the stress based dual formulation of static elastoplasticity the linear kinematic hardening model and the von mises yield condition are used existence and uniqueness of the plastic multiplier is rigorously proved which allows for the reformulation of the forward system using a complementarity condition in order to derive necessary optimality conditions a family of regularized optimal control problems is analyzed wherein the static plasticity problems are replaced by their viscoplastic approximations by passing to the limit in the optimality conditions for the regularized problems necessary optimality conditions of c stationarity type are obtained

heat equation with dynamical boundary conditions of reactive diffusive type this paper deals with the heat equation posed in a bounded reg ular domain of r n n 2 coupled with a dynamical boundary condition of reactive diffusive type in particular we study the problem 8 utu 0 in 0 1 ut ku lu on 0 1 u 0 x u0 x on where u u t x t 0 x 2 x denotes the laplacian operator with respect to the space variable whiledenotes the laplace beltrami operator on is the outward normal to and k and l are given real constants l 0 well posedness is proved for data u0 2 h 1 such that u0 2 h 1 we also study higher regularity of the solution

optimal control for parabolic variational inequalities consider the problem of maximizing a functional that depends on a control function k x t and on the solution u x t of a parabolic variational inequality with k appearing in the data necessary conditions are obtained for the maximizers k 0 x t and the structure of k 0 is then analyzed an application to the stefan problem is given

optimal prestress of cracked unilateral structures finite element analysis of an optimal control problem for variational inequalities abstract the structural analysis problem concerning static stabilization of cracked structures through prestress reinforcement is studied in this paper a linearly elastic structure with given crack interfaces along which frictionless no tension no penetration mechanism hold the so called unilateral contact mechanism is assumed the prestressing control which in most civil engineering applications is realized by externally placed prestressed cables is modelled by means of prestressing control forces the static analysis state problem turns out to be a variational inequality the goal of the stabilization is taken to be the healing of the cracks in the structure with the minimum reinforcement among an available and technologically feasible set and this is expressed by means of a suitably written combined cost function the arising optimal control problem is a nonsmooth and nonconvex one thus appropriate techniques recently developed in the area of nonsmooth analysis are used for its solution numerical examples illustrate the theory and parametric numerical experimentation with various algorithms permit us discuss certain aspects of the computer application appropriate condensation techniques for the reduction of the problem dimensionality and the integration of the studied algorithms in a general purpose finite element software are given

optimal periodic control for the two phase stefan problem consider the two phase stefan problem in a domain x t x in d 0 t infty with the heat flux across a part gamma 1 of partial d being a control function k x t periodic in t of period sigma and n 1 leqq k leqq n 2 int 0 sigma int gamma 1 k x t m where n 1 n 2 m are given positive constants the solution u x t behaves asymptotically as a periodic function hat u x t we wish to maximize int 0 sigma int d p x hat u x t where p is a given positive function it is proved that any optimal control k 0 has the form k 0 x t left begin array 20 c n 2 quad text if 0 t varphi x n 1 quad text if varphi x t sigma end array right where varphi x is a smooth function

differentiability of implicit functions beyond the implicit function theorem abstract the implicit function theorem ift can be used to deduce the differentiability of an implicit mapping s u y given by the equation e y u 0 however the ift is not applicable when different norms are necessary for the differentiation of e w r t y and the invertibility of the partial derivative e y y u we prove theorems ensuring the twice differentiability of the mapping s which can be applied in this case we highlight the application of our results to quasilinear partial differential equations whose principal part depends nonlinearly on the gradient of the state y

distributed control for a class of non newtonian fluids we consider control problems with a general cost functional where the state equations are the stationary incompressible navier stokes equations with shear dependent viscosity the equations are quasi linear the control function is given as the inhomogeneity of the momentum equation in this paper we study a general class of viscosity functions which correspond to shear thinning or shear thickening behavior the basic results concerning existence uniqueness boundedness and regularity of the solutions of the state equations are reviewed the main topic of the paper is the proof of g teaux differentiability which extends known results it is shown that the derivative is the unique solution to a linearized equation moreover necessary first order optimality conditions are stated and the existence of a solution of a class of control problems is shown

index theorems for quantum graphs in geometric analysis an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned sometimes using the heat kernels of two higher order differential operators as an intermediary in this paper the case of quantum graphs is addressed a quantum graph is a graph considered as a singular one dimensional variety and equipped with a second order differential hamiltonian h a laplacian with suitable conditions at vertices for the case of scale invariant vertex conditions i e conditions that do not mix the values of functions and of their derivatives the constant term of the heat kernel expansion is shown to be proportional to the trace of the internal scattering matrix of the graph this observation is placed into the index theory context by factoring the laplacian into two first order operators h a a and relating the constant term to the index of a an independent consideration provides an index formula for any differential operator on a finite quantum graph in terms of the vertex conditions it is also found that the algebraic multiplicity of 0 as a root of the secular determinant of h is the sum of the nullities of a and a

pontryagin maximum principle for optimal control of variational inequalities in this paper we investigate optimal control problems governed by variational inequalities we present a method for deriving optimality conditions in the form of pontryagin s principle the main tools used are the ekeland s variational principle combined with penalization and spike variation techniques

regularity of flows and optimal control of shear thinning fluids abstract we study optimal control problems of systems describing the flow of incompressible shear thinning fluids taking advantage of regularity properties of the flows we derive necessary optimality conditions under a restriction on the optimal control

convergence and optimal control problems of nonlinear evolution equations governed by time dependent operator we study an abstract nonlinear evolution equation governed by a time dependent operator of subdifferential type in a real hilbert space in this paper we discuss the convergence of solutions to our evolution equations also we investigate the optimal control problems of nonlinear evolution equations moreover we apply our abstract results to a quasilinear parabolic pde with a mixed boundary condition

optimal control in some variational inequalities we study a nonconvex nondifferentiable problem of optimal control where the state of the system is defined by an elliptic variational inequality with obstacle and where the cost function is quadr

mathematical programs with complementarity constraints in function space c and strong stationarity and a path following algorithm an optimal control problem governed by an elliptic variational inequality is studied the feasible set of the problem is relaxed and a path following type method is used to regularize the constraint on the state variable first order optimality conditions for the relaxed regularized subproblems are derived and convergence of stationary points with respect to the relaxation and regularization parameters is shown in particular c and strong stationarity as well as variants thereof are studied the subproblems are solved by using semismooth newton methods the overall algorithmic concept is provided and its performance is discussed by means of examples including problems with bilateral constraints and a nonsymmetric operator

maximum principle for optimal control of non well posed elliptic differential equations in this paper we shall study two optimal control problems p1 and p2 governed by some semilinear elliptic di erential equations which can admit more than one solution we shall call such systems non well posed systems we obtain the pontryagin maximum principle for problems p1 and p2 in the 6rst problem p1 the cost functional may be non smooth and the set of controls is convex while in the second problem p2 the cost functional is smooth and the set of controls is non convex in both problem p1 and problem p2 we consider some state constraint of integral type due to some practical interests many authors studied optimal control for elliptic di erential equations here we cite 1 10 12 15 however most of these works except for 7 10 13 deal with state equations which are governed by monotone operators and admit a unique solution corresponding to each control in such problems the pontryagin maximum principle was obtained by studying the variations of the state with respect to some perturbations of the control cf 1 2 12 15 in the present work the state equations are governed by non monotone operators and can admit more than one solution we cannot obtain the variations of the state with respect to the control with the same methods in 1 2 12 15 when the state equations admit more than one solution we even do not know how to make the sensitivity analysis of the state with respect to the control

first order optimality conditions for elliptic mathematical programs with equilibrium constraints via variational analysis mathematical programs in which the constraint set is partially defined by the solutions of an elliptic variational inequality so called elliptic mpecs are formulated in reflexive banach spaces with the goal of deriving explicit first order optimality conditions amenable to the development of numerical procedures variational analytic concepts are both applied and further developed the paper is split into two main parts the first part concerns the derivation of conditions in which the lower level state constraints are assumed to be polyhedric sets this part is then completed by two examples the latter of which involves pointwise bilateral bounds on the gradient of the state the second part focuses on an important nonpolyhedric example namely when the lower level state constraints are presented by pointwise bounds on the euclidean norm of the gradient of the state a formula for the second order mosco epiderivative of the indicator function for this convex set is derived this result is then used to demonstrate the hadamard directional differentiability of the solution mapping of the variational inequality which then leads to the derivation of explicit strong stationarity conditions for this problem

indirect obstacle control problem for semilinear elliptic variational inequalities an optimal control problem for a coupled system of a semilinear elliptic equation and an obstacle variational inequality is considered existence and optimality conditions of optimal triple are established

on the regularity of an obstacle control problem an optimal control problem of the obstacle for an elliptic variational inequality is considered in which the obstacle is regarded as the control to get the regularity of the optimal pair a new related control problem is introduced by proving the existence of an optimal pair to such a new control problem the regularity of the optimal pair to the original problem is obtained it turns out that the regularity obtained is sharp in general some other interesting properties of the optimal pair are also established

a self adaptive co ordinate transformation for efficient numerical evaluation of general boundary element integrals almost all general purpose boundary element computer packages include a curved geometry modelling capability thus numerical quadrature schemes play an important role in the efficiency of programming the technique the present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two dimensional axisymmetric and three dimensional applications emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of gaussian quadrature scheme s within the near singularity range the procedure can easily be implemented into existing be codes and presents the important feature of being self adaptive i e it produces a variable lumping of the gauss stations toward the singularity depending on the minimum distance from the source point to the element the self adaptiveness of the scheme also makes it inactive when not useful large source distances which makes it very safe for general usage

boundary optimal control for quasistatic bilateral frictional contact problems abstract we consider a mathematical model describing the quasistatic process of bilateral contact with friction between an elastic body and a rigid foundation our goal is to study a related optimal control problem which allows us to obtain a desired field of displacements on the contact boundary by acting with a control on another part of the boundary of the body using penalization and regularization techniques we derive the necessary conditions of optimality

bilateral obstacle optimal control for a quasilinear elliptic variational inequality with a source term abstract in this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality with a source term and the control functions are the upper and the lower obstacles we assume that the obstacles and are in w 2 2 but this causes difficulty for deriving the optimality condition by applying the weak convergence method we establish existence and incomplete necessary conditions for the optimal control

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

well posedness and symmetries of strongly coupled network equations we consider a class of evolution equations taking place on the edges of a finite network and allow for feedback effects between different possibly non adjacent edges this generalizes the setting that is common in the literature where the only considered interactions take place at the boundary i e in the nodes of the network we discuss well posedness of the associated initial value problem as well as contractivity and positivity properties of its solutions finally we discuss qualitative properties that can be formulated in terms of invariance of linear subspaces of the state space i e of symmetries of the associated physical system applications to a neurobiological model as well as to a system of linear schrodinger equations on a quantum graph are discussed

the spectrum of the hilbert space valued second derivative with general self adjoint boundary conditions abstract we consider a large class of self adjoint elliptic problems associated with the second derivative acting on a space of vector valued functions we present and survey several results that can be obtained by means of two different approaches to the study of the associated eigenvalues problems the first more general one allows to replace a secular equation which is well known in some special cases by an abstract rank condition the second one though available in general seems to apply particularly well to a specific boundary condition the sometimes dubbed anti kirchhoff condition in the literature that arises in the theory of differential operators on graphs it also permits to discuss interesting and more direct connections between the spectrum of the differential operator and some graph theoretical quantities in particular some results on the symmetry of the spectrum in either case

optimal control of parabolic differential equations with two point boundary state constraints this paper deals with the necessary conditions of optimality for some optimal control problems governed by some parabolic differential equations involving monotone graphs the two point boundary time variable state constraints are discussed some analyses on the state equations are given

optimal control of shear thickening flows we study optimal control problems of systems describing the flow of incompressible shear thickening fluids we prove existence of solutions and derive necessary optimality conditions under precise restrictions on the optimal control

a posteriori error estimates for optimal control problems governed by parabolic equations in this paper we derive a posteriori error estimates for the finite element approximation of quadratic optimal control problem governed by linear parabolic equation we obtain a posteriori error estimates for both the state and the control approximation such estimates which are apparently not available in the literature are an important step towards developing reliable adaptive finite element approximation schemes for the control problem

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

semi analytic treatment of the three dimensional poisson equation via a galerkin bie method a systematic treatment of the three dimensional poisson equation via singular and hypersingular boundary integral equation techniques is investigated in the context of a galerkin approximation developed to conveniently deal with domain integrals without a volume fitted mesh the proposed method initially converts domain integrals featuring the newton potential and its gradient into equivalent surface integrals then the resulting boundary integrals are evaluated by means of well established cubature methods in this transformation weakly singular domain integrals defined over simply or multiply connected domains with lipschitz boundaries are rigorously converted into weakly singular surface integrals combined with the semi analytic integration approach developed for potential problems to accurately calculate singular and hypersingular galerkin surface integrals this technique can be employed to effectively deal with mixed boundary value problems without the need to partition the underlying domain into volume cells sample problems are included to validate the proposed approach

minimax control for evolutionary variational bilateral problem this paper deals with a minimax control problem for semilinear evolutionary variational inequalities associated with bilateral constraints the control domain is not necessarily convex the cost functional which is to be minimized is the sup norm of some function of the state and the control the major novelty of such a problem lies in the simultaneous presence of the nonsmooth state equation variational inequality and the nonsmooth cost functional the sup norm in this paper the existence and the pontryagin type necessary condition for optimal controls are established

c1 α local regularity of weak solutions of degenerate elliptic equations abstract it is demonstrated the local c 1 alpha nature of weak solutions of elliptic equations of the type 1 1 in the introduction under the degeneracy or singularity assumptions a sub 1 a sub 3

optimal control of quasilinear parabolic equations this paper deals with optimal control problems governed by quasilinear parabolic equations in divergence form whose cost functional is of lagrangian type our aim is to prove the existence of solutions and derive some optimality conditions to attain this second objective we accomplish the sensitivity analysis of the state equation with respect to the control proving that under some assumptions this relation is g teaux differentiable finally a regularising procedure along with ekeland s variational principle allow us to treat some other problems for which this differentiability property cannot be stated

the multiple reciprocity boundary element method in elasticity a new approach for transforming domain integrals to the boundary this technique operates on domain integrals resulting from different types of body forces such as gravitational and centrifugal forces as well as loadings due to linear and quadratic temperature distributions

boundary integral approximation of volume potentials in three dimensional linear elasticity a systematic treatment of volume potentials appearing in a boundary integral equation formulation of the three dimensional lame equation is rigorously investigated and its usefulness demonstrated in the context of a collocation boundary element method developed to effectively deal with volume potentials without a volume fitted mesh the proposed approach initially converts elastic volume potentials defined in the form of domain integrals featuring a non trivial body force into equivalent surface integrals then the resulting boundary integrals are evaluated by means of well established cubature methods details of these domain to boundary integral transformations are provided along with some examples to show the correctness of the calculation of the elastic newton potential moreover with the aid of an analytic integration technique developed to accurately compute singular surface integrals in linear elasticity numerical examples dealing with mixed boundary value problems for the three dimensional lame equation are included to validate the proposed approach

optimal control of shear thinning fluids the aim of this paper is to establish necessary optimality conditions for optimal control problems governed by steady incompressible navier stokes equations with shear dependent viscosity the main difficulty is related to the differentiability of the control to state mapping and is overcome by introducing a family of smooth approximate control problems and by passing to the limit in the corresponding optimality conditions

error estimates for optimal control problems of a class of quasilinear equations arising in variable viscosity fluid flow we consider optimal control problems of quasilinear elliptic equations with gradient coefficients arising in variable viscosity fluid flow the state equation is monotone and the controls are of distributed type we prove that the control to state operator is twice frechet differentiable for this class of equations a finite element approximation is studied and an estimate of optimal order h is obtained for the control the result makes use of the distributed structure of the controls together with a regularity estimate for elliptic equations with holder coefficients and a second order sufficient optimality condition the paper ends with a numerical experiment where the approximation order is computationally tested

a data assimilation approach for non newtonian blood flow simulations in 3d geometries abstract blood flow simulations can play an important role in medical training and diagnostic predictions associated to several pathologies of the cardiovascular system the main challenge at the present stage is to obtain reliable numerical simulations in the particular districts of the cardiovascular system that we are interested in here we propose a data assimilation procedure in the form of a non linear optimal control problem of dirichlet type to reconstruct the blood flow profile from known data available in certain parts of the computational domain this method will allow us to obtain the boundary conditions not fully determined by the physics of the model in order to recover more accurate simulations to solve the control problem we propose a discretize then optimize do approach based on a stabilized finite element method numerical simulations on 3d geometries are performed to validate this procedure in particular we consider some idealized geometries of interest and real geometries such as a saccular aneurysm and a bypass we assume blood as an homogeneous fluid with non newtonian inelastic shear thinning behavior the results show that even in the presence of noisy data accuracy can be improved using the optimal control approach

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

nurbs enhanced line integration boundary element method for 2d elasticity problems with body forces abstract a nurbs enhanced boundary element method for 2d elasticity problems with body forces is proposed in this paper the non uniform rational b spline nurbs basis functions are applied to construct the geometry and the model can be reproduced exactly at all stages since the refinement will not change the shape of the boundary both open curves and closed curves are considered the fields are approximated by the traditional lagrangian basis functions in parameter space rather than by the same nurbs basis functions for geometry approximation the parametric boundary elements and collocation nodes are defined from the knot vector of the curve and the refinement of the nurbs curve is easy boundary conditions can be imposed directly since the lagrangian basis functions have the property of delta function in addition most methods for the treatment of singular integrals in traditional boundary element method can be applied in the proposed method to overcome the difficulty for evaluation of the domain integrals in problems with body forces a line integration method is further applied in this paper to compute the domain integrals without additional volume discretizations numerical examples have shown the accuracy of the proposed method

distributed control of systems governed by a general class of quasilinear elliptic equations abstract in this paper we are concerned with optimal control problems governed by a general class of quasilinear elliptic equations our aim is to prove existence of solution and derive optimality conditions in order to deal with this last question we begin investigating differentiability of state solution of equation with respect to the control second term of equation obtaining it only in certain cases a perturbation method is used to treat other cases as a consequence of the optimality system regularity of optimal control and state is establised

optimality conditions for control problems governed by variational inequalities this paper deals with the theory of first order necessary conditions of optimality for nonsmooth control problems governed by variational inequalities we present a general approach in which necessary conditions of first order are obtained by means of differentiation tools based on epi convergence of second order differential quotients

on the optimal control of variational hemivariational inequalities abstract the present paper represents a continuation of 26 there a continuous dependence result for the solution of an elliptic variational hemivariational inequality was obtained and then used to prove the existence of optimal pairs for two associated optimal control problems in the current paper we complete this study with more general results indeed we prove the continuous dependence of the solution with respect to a parameter which appears in all the data of the problem including the set of constraints the nonlinear operator and the two functionals which govern the variational hemivariational inequality this allows us to consider a general associated optimal control problem for which we prove the existence of optimal pairs together with a new convergence result the mathematical tools developed in this paper are useful in the analysis and control of a large class of boundary value problems which in a weak formulation lead to elliptic variational hemivariational inequalities to provide an example we illustrate our results in the study of an inequality which describes the equilibrium of an elastic body in frictional contact with a foundation made of a rigid body covered by a layer of soft material

some regularity results for p harmonic mappings between riemannian manifolds abstract let m be a c 2 smooth riemannian manifold with boundary and n a complete c 2 smooth riemannian manifold we show that each stationary p harmonic mapping u m n whose image lies in a compact subset of n is locally c 1 for some 0 1 provided that n is simply connected and has non positive sectional curvature we also prove similar results for minimizing p harmonic mappings with image being contained in a regular geodesic ball moreover when m has non negative ricci curvature and n is simply connected with non positive sectional curvature we deduce a gradient estimate for c 1 smooth weakly p harmonic mappings from which follows a liouville type theorem in the same setting

optimal control of the obstacle in a quasilinear elliptic variational inequality abstract in this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality and the control function is the obstacle the state is chosen to be close to the desire profile while the h 2 norms of the obstacle is not too large existence and necessary conditions for the optimal control are established

optimal control for variational inequalities consider the problem of maximizing a functional which depends on a control function k and on the solution of an elliptic variational inequality with k appearing in the data the variational problem for k is nondiflerentiable and nonconvex we obtain necessary conditions on a maximizes k 0 and then use them to determine the structure of k 0 in some cases

necessary conditions for optimal control of distributed parameter systems the ekeland variational principle is used to prove a maximum principle for the optimal controls of a general semilinear evolutionary control system in a banach space with strictly convex dual the boundary constraint is of general type which includes the optimal periodic control problem as a special case

feedback stabilization and optimal control for the cahn hilliard equation this paper is concerned with the control problem for the cahn hilliard equation 4 the physical background is as follows suppose there is a binary solution in a container sz c ir n 5 3 and suppose the mole fraction of the a component is u then the mole fraction for the other component b is 1 u it is well known that the function u of x e sz and t 1 0 due to mass conservation satisfies the cahn hilliard equation 4 u ya2u ap u in sz x r 1 1 where y 0 is a small positive constant and typically p u u3 24 1 2 suppose u has spatial distribution uo x initially i e u x 0 u x 1 3 then the evolution of u x t is determined by 1 l 1 3 and the boundary conditions au i i aau o an x 1 4

control of free boundary problem with hysteresis we consider the problem of controlling the free boundary of the two phase stefan problem by means of boundary hysteresis control based on the preisach model it is proved that for each control mu there is a corresponding solution of the stefan problem and that there exists an optimal control

local a posteriori error estimates for convex boundary control problems in this paper we derive some improved a posteriori error estimates for finite element approximation of neumann boundary control problems we first establish local upper a posteriori error estimates for both the state and the control approximation of the general convex boundary control problems we then derive local upper and lower a posteriori error estimates for a class of control problems that frequently appear in applications

computational aspects in 2d sbem analysis with domain inelastic actions the symmetric boundary element method applied to structures subjected to temperature and inelastic actions shows singular domain integrals in the present paper the strong singularity involved in the domain integrals of the stresses and tractions is removed and by means of a limiting operation this traction is evaluated on the boundary first the weakly singular domain integral in the somigliana identity s i of the displacements is regularized and the singular integral is transformed into a boundary one using the radial integration method subsequently using the differential operator applied to the displacement field the s i of the tractions inside the body is obtained and through a limit operation its expression is evaluated on the boundary the latter operation makes it possible to substitute the strongly singular domain integral in a strongly singular boundary one defined as a cauchy principal value with which the related free term is associated the expressions thus obtained for the displacements and the tractions in which domain integrals are substituted by boundary integrals were utilized in the galerkin approach for the evaluation in closed form of the load coefficients connected to domain inelastic actions this strategy makes it possible to evaluate the load coefficients avoiding considerable difficulties due to the geometry of the solid analyzed the obtained coefficients were implemented in the karnak sgbem calculus code copyright 2009 john wiley sons ltd

some optimality conditions of quasilinear elliptic obstacle optimal control problems this paper is concerned with an obstacle optimal control problem for a quasilinear elliptic variational inequality with a source term the pth power of laplacian of the obstacle appears in the cost functional this feature leads that it is hard to derive the optimality system for the underlying problem the existence for the optimal control is proved and we also show how to obtain optimality system using a passage to the limit in the approximation process

a posteriori error estimates for some model boundary control problems in this paper we derive a posteriori error estimates for the finite element approximation of quadratic optimal boundary control problems we derive a posteriori error estimates for both the state and the control approximation on polygonal domains such estimates which are apparently not available in the literature can be used to construct reliable adaptive finite element approximation schemes for the control problems

optimal control of problems governed by abstract elliptic variational inequalities with state constraints in this paper we investigate optimal control problems governed by elliptic variational inequalities with additional state constraints we present a relaxed formulation for the problem with penalization methods and approximation techniques we give qualification conditions to get first order optimality conditions

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

maximum principle of optimal control for degenerate quasi linear elliptic equations optimal control problems governed by degenerate quasi linear partial differential equations of elliptic type are considered the optimal control systems considered may lack cesari type conditions and therefore the corresponding approximate optimal control problem may have no solution to yield the maximum principle of optimal pairs relaxed controls are used to overcome the difficulties occurring when considering approximate problems the relaxed controls used are defined by finite additive measures so that the case of the control set being noncompact can be treated

boundary element analysis in thermoelasticity with and without internal cells in this paper a set of internal stress integral equations is derived for solving thermoelastic problems a jump term and a strongly singular domain integral associated with the temperature of the material are produced in these equations the strongly singular domain integral is then regularized using a semi analytical technique to avoid the requirement of discretizing the domain into internal cells domain integrals included in both displacement and internal stress integral equations are transformed into equivalent boundary integrals using the radial integration method rim two numerical examples for 2d and 3d respectively are presented to verify the derived formulations copyright 2003 john wiley sons ltd

optimal boundary control of a viscous cahn hilliard system with dynamic boundary condition and double obstacle potentials in this paper we investigate optimal boundary control problems for cahn hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the laplace beltrami operator the cost functional is of standard tracking type and box constraints for the controls are prescribed we prove existence of optimal controls and derive first order necessary conditions of optimality the general strategy which follows the lines of the recent approach by colli farshbaf shaker and sprekels appl math optim 71 2015 pp 1 24 to the simpler allen cahn case is the following we use the results that were recently established by colli gilardi and sprekels appl math optim online first doi 10 1007 s00245 015 9299 z 2015 for the case of differentiable logarithmic potentials and perform a so called deep quench limit using compactness and monotonicity arguments it is shown that this strategy leads to the desired first order necessary optimality conditions for t

an optimal control problem governed by quasi linear variational inequalities an optimal control problem governed by quasi linear variational inequality is considered the cost functional to be minimized contains the solution of a quasi linear variational inequality to get the existence regularity and necessary condition for the optimal pair a new related control problem is introduced by proving the existence of an optimal pair to such a new problem the existence and regularity of the optimal pair to the original problem are obtained it turns out that the regularity obtained is sharp in general some necessary conditions of the optimal pair are also obtained

maximizing the output energy of a linear channel with a time and amplitude limited input the problem of maximizing the output energy of a linear time invariant channel given that the input signal is time and amplitude limited is considered it is shown that a necessary condition for an input mu to be optimal assuming a unity amplitude constraint is that it satisfy the fixed point equation sgn f mu where the functional f is the convolution of mu with the autocorrelation function of the channel impulse response it is also shown that all solutions to this equation for which mod mu mod 1 almost everywhere correspond to local maxima of the output energy iteratively recomputing mu from the fixed point equation leads to an algorithm for finding local optima numerical results are given for the cases where the transfer function is ideal low pass and has two poles these results support the conjecture that in the ideal low pass case the optimal input signal is a single square pulse a generalization of the preceding fixed point condition is also derived for the problem of maximally separating n outputs of a discrete time linear time invariant channel