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Preprint 28-2008

Optimal boundary control of a system of semilinear parabolic equations

Source file is available as :   Portable Document Format (PDF)

Author(s) : Werner Barthel, Christian John , Fredi Tröltzsch

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 28-2008

MSC 2000

49J20 Optimal control problems involving partial differential equations
35K57 Reaction-diffusion equations

Abstract :
In this work, boundary control problems governed by a system of semilinear parabolic PDEs with pointwise control constraints are considered. This class of problems is related to applications in the chemical catalysis. After discussing existence and uniqueness of the state equation with both linear and nonlinear boundary conditions, the existence of an optimal solution is shown. Necessary and sufficient optimality conditions are derived to deal with numerical examples, which conclude the paper.

Keywords : Optimal boundary control,semilinear parabolic system,necessary optimality conditions, sufficient optimality conditions

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