Relaxation of Optimal Control Problem Governed by Semilinear Elliptic Equation with Leading Term Containing Controls

An optimal control problem governed by semilinear elliptic partial differential equation is considered. The equation is in divergence form with the leading term containing controls. A relaxed problem is constructed by homogenization. By studying the G -closure problem, a local representation of admi...

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Veröffentlicht in:	Acta applicandae mathematicae 2014-04, Vol.130 (1), p.205-236
Hauptverfasser:	Li, Bo, Lou, Hongwei, Xu, Yashan
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Applied mathematics Calculus of Variations and Optimal Control Optimization Computational Mathematics and Numerical Analysis Control equipment Control theory Euclidean space Homogenization Homogenizing Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Maximum principle Optimal control Partial Differential Equations Probability Theory and Stochastic Processes Representations Spikes Studies Theorems
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Zusammenfassung:	An optimal control problem governed by semilinear elliptic partial differential equation is considered. The equation is in divergence form with the leading term containing controls. A relaxed problem is constructed by homogenization. By studying the G -closure problem, a local representation of admissible set of relaxed control is given. Finally, the maximum principle of relaxed problem is established via homogenization spike variation.
ISSN:	0167-8019 1572-9036
DOI:	10.1007/s10440-013-9843-2