This paper presents the numerical solution of a constrained optimal control problem (COCP) for quasilinear parabolic equations. The COCP is converted to unconstrained optimization problem (UOCP) by applying the exterior penalty function method. Necessary optimality conditions for the considered problem are established. The computing optimal controls are helped to identify the unknown coefficien...

Abstract The paper investigates stability properties of solutions optimal control problems constrained by semilinear parabolic partial differential equations. Hölder or Lipschitz dependence the solution on perturbations are obtained for in which equation and objective functional affine with respect to control. may appear both nonlinearly depend state variables. main results based an extension r...

Nonconvex optimal control problems governed by evolution in infinite-dimensional spaces (as, e.g., parabolic boundary-value problems) needs a continuous (and possibly also smooth) extensio...

pontryagin's principle is used to study the shape of the supersonic part of the nozzle of a carbon dioxide gas-dynamic laser whose gain is maximal. the exact shape is obtained for the uncoupled approximation of anderson's bimodal model. in this case, if sharp corners are allowed, the ceiling of the supersonic part consists of a slant rectangular sheet followed by a horizontal one; oth...

The paper is concerned with the optimal harvesting of a marine park, which is described by a parabolic heat equation with Neumann boundary conditions and a nonlinear source term. We consider a cost functional, which is linear with respect to the control; hence the optimal solution can belong to the class of measure-valued control strategies. For each control function, we prove existence, and st...