Abstract
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.
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The authors are heartily grateful to the anonymous referees for their valuable comments and suggestions.
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This work was supported in part by 973 Program (No. 2011CB808002) and NSFC (No. 61074047).
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Li, B., Lou, H. & Xu, Y. Relaxation of Optimal Control Problem Governed by Semilinear Elliptic Equation with Leading Term Containing Controls. Acta Appl Math 130, 205–236 (2014). https://doi.org/10.1007/s10440-013-9843-2
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DOI: https://doi.org/10.1007/s10440-013-9843-2