Abstract
In this paper the support of a Radon measure is selected in an optimal way. The solution of the parabolic equation depends on the measure via the mixed type boundary conditions. The existence of a solution for a class of domain optimization problems is shown. We also investigate the behavior of the optimal solution for some time T,when T → ∞ and we prove that it converges to the optimal solution of the stationary problem. The first order necessary optimality conditions are derived.
This research was supported for J.S. by INRIA-Lorraine and the Systems Research Institute of the Polish Academy of Sciences.
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Henrot, A., Sokołowski, J. (1998). A Shape Optimization Problem for the Heat Equation. In: Optimal Control. Applied Optimization, vol 15. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6095-8_10
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DOI: https://doi.org/10.1007/978-1-4757-6095-8_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4796-3
Online ISBN: 978-1-4757-6095-8
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