On the Semigroup Approach for the Optimal Control of Semilinear Parabolic Equations Including Distributed and Boundary Control
Fredi Tröltzsch · Zeitschrift für Analysis und ihre Anwendungen · 1989
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.