Abstract. 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 associat...

In this paper, we provide results concerning the optimal feedback control of a system of partial di erential equations which arises within the context of modelling a particular uid/structure interaction system seen in structural acoustics, this application being the primary motivation for our work. This model onsists of two coupled PDE's exhibiting parabolic and hyperbolic characteristics respe...

This paper is the second part of our work on a priori error analysis for finite element discretizations of parabolic optimal control problems. In the first part [18] problems without control constraints were considered. In this paper we derive a priori error estimates for space-time finite element discretizations of parabolic optimal control problems with pointwise inequality constraints on the...

We present a non-overlapping spatial domain decomposition method for the solution of linear–quadratic parabolic optimal control problems. The spatial domain is decomposed into non-overlapping subdomains. The original parabolic optimal control problem is decomposed into smaller problems posed on space-time cylinder subdomains with auxiliary state and adjoint variables imposed as Dirichlet bounda...

This paper presents the multiharmonic analysis of a distributed parabolic optimal control problem in a time-periodic setting. We prove the existence and uniqueness of the solution of some weak space-time variational formulation for the parabolic time-periodic boundary value problem appearing in the constraints for the optimal control problem. Since the cost functional is quadratic, the optimal ...

In this paper, we study optimal control problems for parabolic hemivariational inequalities of dynamic elasticity and investigate the continuity of the solution mapping from the given initial value and control data to trajectories. We show the existence of an optimal control which minimizes the quadratic cost function and establish the necessary conditions of optimality of an optimal control fo...

In the paper we investigate solvability of nonlinear optimal Thermal and Diffusion processes control problems defined by semi-linear parabolic equations when the source function nonlinearly depends on the controlling parameters, and nonlinear integral criterion of quality is minimized. We obtained the sufficient conditions of uniqueness of the solution of the boundary value problem and the adjo...

Various optimization problems associated with the optimal control of distributed parabolic systems with time delays appearing in boundary conditions were studied recently by Wang (1975), Knowles (1978), Kowalewski (1988; 1990a;1990b; 1998; 1999; 2001), Kowalewski and Duda (1992) and Kowalewski and Krakowiak (2000). In (Wang, 1975), optimal control problems for parabolic systems with Neumann bou...

in an axisymmetric co2-n2-h2o gas dynamic laser, let ? denote the intersection of the vertical plane of symmetry with the upper part of the (supersonic) nozzle. to obtain a maximal small signal gain, some authors have tested several families of curves for ?. to find the most general solution for ?, an application of pontryagin’s principle led to the conjuncture that the optimal ? must consist o...