Optimal boundary control of a system of reaction diffusion equations

• Published in: Zeitschrift für angewandte Mathematik und Mechanik 2010-12, Vol.90 (12), p.966-982
• Main Authors: Barthel, W., John, C., Tröltzsch, F.
• Format: Article
• Language: English
• Subjects: boundary control; Calculus of variations and optimal control; Exact sciences and technology; Mathematical analysis; Mathematics; necessary optimality conditions; Nonlinear algebraic and transcendental equations; Numerical analysis; Numerical analysis. Scientific computation; Optimal control; Partial differential equations; reaction-diffusion equations; Sciences and techniques of general use; semilinear parabolic system; sufficient optimality conditions
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.200900359

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. 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.