×

zbMATH — the first resource for mathematics

Optimal boundary control of a system of reaction diffusion equations. (English) Zbl 1375.49030
Summary: 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.

MSC:
49K20 Optimality conditions for problems involving partial differential equations
35K57 Reaction-diffusion equations
49M30 Other numerical methods in calculus of variations (MSC2010)
49N10 Linear-quadratic optimal control problems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] R. Aris
[2] Casas, SIAM J. Control Optim. 35 pp 1297– (1997)
[3] Z. Chen K.H. Hoffmann
[4] R. Griesse
[5] Griesse, SIAM J. Control Optim. 44(2) pp 467– (2005)
[6] Heinkenschloss, Optimization Methods and Software 7 pp 211– (1997)
[7] M. Heinkenschloss E.W. Sachs
[8] M.A. Liauw M. Baerns R. Broucek O. Buyevskaya J.M. Commenge J.P. Corriou K. Gebauer H.J. Hefter O.U. Langer M. Matlosz A. Renken A. Rouge R. Schenk N. Steinfeldt S. Walter
[9] I. Neitzel U. Prüfert T. Slawig
[10] Neitzel, Numer. Algorithms 50(3) pp 241– (2009)
[11] C. Pao
[12] Raymond, Appl. Math. Optim. 39 pp 143– (1999)
[13] Sachs, Z. Angew. Math. Mech. 58 pp 443– (1978)
[14] F. Tröltzsch
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.