test fields on compact space times in this paper some basic aspects of lorentzian field theory on compact lorentz manifolds are studied all compact space times are acausal i e possess closed timelike curves this makes them a useful testbed in analyzing some new notions of causality that will be introduced for more general acausal space times in addition studying compact space times in their own right raises a wide range of fascinating mathematical problems some of which will be explored it will be shown that it is reasonable to expect lorentzian field theory on a compact space time to provide information on the topology of the underlying manifold if this is true then this information is likely to be orthogonal or complementary to the information obtained through the study of euclidean field theory

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

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

maximum principle of state constrained optimal control governed by fluid dynamic systems this work deals with maximum principle of optimal control governed by some fluid dynamic systems which include three dimensional navier stokes equations some type of state constraint is involved

optimal control of damped klein gordon equations with state constraints abstract in this paper we study the maximum principles for optimal control problems governed by the damped klein gordon equations with state constraints and we prove the existence of the optimal parameter and deduce the necessary conditions on the optimal parameter

optimal control of pdes in a complex space setting application to the schrodinger equation in this paper we discuss optimality conditions for abstract optimization problems over complex spaces we then apply these results to optimal control problems with a semigroup structure as an application we detail the case when the state equation is the schrodinger one with pointwise constraints on the bilinear control we derive first and second order optimality conditions and address in particular the case that the control enters the state equation and cost function linearly

optimal controls of 3 dimensional navier stokes equations with state constraints this work is concerned with the maximum principles for optimal control problems governed by 3 dimensional navier stokes equations some types of state constraints time variables are considered

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

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 control of infinite dimensional bilinear systems application to the heat and wave equations in this paper we consider second order optimality conditions for a bilinear optimal control problem governed by a strongly continuous semigroup operator the control entering linearly in the cost function we derive first and second order optimality conditions taking advantage of the goh transform we then apply the results to the heat and wave equations

pontryagin maximum principle of optimal control governed by fluid dynamic systems with two point boundary state constraint over all y u y mad 0 t u subject to the semilinear equation y t ay t by t du t f t a e t 0 t 1 1 with state constraint y 0 y t s 1 2 the following hypotheses will be e9ective throughout this paper h1 v and h are real hilbert spaces with norms and moreover v h v algebraically and topologically with compact injections where v denotes the dual of

on the stability of functional equations in banach spaces the paper is devoted to some results on the problem of s m ulam for the stability of functional equations in banach spaces the problem was posed by ulam 60 years ago

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

optimal pointwise control for a parallel system of euler bernoulli beams abstract the optimal control of a distributed system consisting of two euler bernoulli beams coupled in parallel with pointwise controllers is considered an index of performance is formulated which consists of a modified energy functional of two coupled structures at a specified time and penalty functions involving the point control forces the minimization of the performance index over these forces is subject to the equation of motion governing the structural vibrations the imposed initial condition as well as the boundary conditions a maximum principle is derived for optimal point controls of one dimensional coupled structures undergoing transverse vibrations the optimal control law is obtained using a maximum principle and the applicability of the results is demonstrated a method of solution for such a type of structure is suggested by using the eigenfunction expansion and the maximum principle the solution involves reducing the original problem to a system of ordinary differential equations the effectiveness of this approach is illustrated numerically by comparing the behavior of the controlled and uncontrolled problem

stabilization of the boussinesq equation via internal feedback controls in this paper we show that the steady state solutions to boussinesq equations in three dimensional domain are stabilizable by internal controllers with the supports in subsets 1 under some conditions on and 1

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

stability of c inner products abstract in this paper we investigate the stability of the inner products in hilbert c modules over unital c algebras

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

some results on stability of extended derivations abstract in this paper we prove the generalized hyers ulam rassias stability of extended derivations on unital banach algebras associated to a generalized jensen equation

necessary and sufficient conditions for optimal controls in viscous flow problems a class of optimal control problems in viscous flow is studied main results are the pontryagin maximum principle and the verification theorem for the hamilton jacobi bellman equation characterising the feedback problem the maximum principle is established by two quite different methods

canonical variation of a lorentzian metric abstract given a lorentzian manifold m g l and a timelike unitary vector field e we can construct the riemannian metric g r g l 2 being the metrically equivalent one form to e we relate the curvature of both metrics especially in the case of e being killing or closed and we use the relations obtained to give some results about m g l

local internal controllability of the boussinesq system in this paper we shall show that the h3 h3 steady state solutions to boussinesq equations in n dimensional bounded domain n 2 3 are locally controllable by internal controllers with the support in subsets

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

optimal controls of boussinesq equations with state constraints abstract this work is concerned with the maximum principle for an optimal control problem governed by boussinesq equations some integral type state constraints are considered

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

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

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

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

a berger green type inequality for compact lorentzian manifolds we give a lorentzian metric on the null congruence associated with a timelike conformal vector field a liouville type theorem is proved and a boundedness for the volume of the null congruence analogous to a well known berger green theorem in the riemannian case will be derived by studying conjugate points along null geodesics as a consequence several classification results on certain compact lorentzian manifolds without conjugate points on its null geodesics are obtained finally several properties of null geodesics of a natural lorentzian metric on each odd dimensional sphere have been found

periodic geodesics and geometry of compact lorentzian manifolds with a killing vector field we study the geometry and the periodic geodesics of a compact lorentzian manifold that has a killing vector field which is timelike somewhere using a compactness argument for subgroups of the isometry group we prove the existence of one timelike non self intersecting periodic geodesic if the killing vector field is nowhere vanishing then there are at least two distinct periodic geodesics as a special case compact stationary manifolds have at least two periodic timelike geodesics we also discuss some properties of the topology of such manifolds in particular we show that a compact manifold m admits a lorentzian metric with a nowhere vanishing killing vector field which is timelike somewhere if and only if m admits a smooth circle action without fixed points

optimal control of semilinear parabolic systems with state constraint abstract the aim of this work is to obtain the existence of optimal solution and maximum principle for optimal control problem with pointwise type state constraint governed by semilinear parabolic systems with certain polynomial like nonlinearity application to optimal control problems of the phase transition system is given

non localization of eigenfunctions for sturm liouville operators and applications in this article we investigate a non localization property of the eigenfunctions of sturm liouville operators a a partial xx a cdot operatorname id with dirichlet boundary conditions where a cdot runs over the bounded nonnegative potential functions on the interval 0 l with l 0 more precisely we address the extremal spectral problem of minimizing the l 2 norm of a function e cdot on a measurable subset omega of 0 l where e cdot runs over all eigenfunctions of a a at the same time with respect to all subsets omega having a prescribed measure and all l infty potential functions a cdot having a prescribed essentially upper bound we provide some existence and qualitative properties of the minimizers as well as precise lower and upper estimates on the optimal value several consequences in control and stabilization theory are then highlighted