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Zeitschrift für Analysis und ihre Anwendungen


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Volume 8, Issue 5, 1989, pp. 431–443
DOI: 10.4171/ZAA/364

Published online: 1989-10-31

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

Fredi Tröltzsch[1]

(1) Technische Universität Berlin, Germany

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.

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Tröltzsch Fredi: On the Semigroup Approach for the Optimal Control of Semilinear Parabolic Equations Including Distributed and Boundary Control. Z. Anal. Anwend. 8 (1989), 431-443. doi: 10.4171/ZAA/364