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Optimal boundary control of a system of reaction diffusion equations
Author(s) -
Barthel W.,
John C.,
Tröltzsch F.
Publication year - 2010
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200900359
Subject(s) - pointwise , uniqueness , mathematics , boundary (topology) , work (physics) , nonlinear system , optimal control , mathematical analysis , class (philosophy) , boundary value problem , reaction–diffusion system , parabolic partial differential equation , partial differential equation , mathematical optimization , computer science , physics , thermodynamics , quantum mechanics , artificial intelligence
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.