On the Semigroup Approach for the Optimal Control of Semilinear Parabolic Equations Including Distributed and Boundary Control

Abstract

The concept of mild solutions and the variation of constants formula are applied to derive first-order necessary conditions for optimal control problems governed by semilinear parabolic initial-boundary value problems. An adjoint system is defined by means of an abstract integral equation, the solution of the latter being a mild solution of an adjoint parabolic equation.