Optimal Control of Two-Phase Membrane Problem
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910450711527424 |
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| author | Bozorgnia, Farid Kungurtsev, Vyacheslav |
| author_facet | Bozorgnia, Farid Kungurtsev, Vyacheslav |
| contents | We consider an optimal control problem where the state is governed by a free boundary problem called the two-phase membrane problem and the control appears in the coefficients of the characteristic function of the positivity and negativity parts of the solution. Our investigation focuses on various properties associated with the control-to-state map. Due to the non-differentiability of this map, we regularize the state equation. The existence, uniqueness, and characterization of the optimal pairs are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10704 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Control of Two-Phase Membrane Problem Bozorgnia, Farid Kungurtsev, Vyacheslav Optimization and Control Analysis of PDEs We consider an optimal control problem where the state is governed by a free boundary problem called the two-phase membrane problem and the control appears in the coefficients of the characteristic function of the positivity and negativity parts of the solution. Our investigation focuses on various properties associated with the control-to-state map. Due to the non-differentiability of this map, we regularize the state equation. The existence, uniqueness, and characterization of the optimal pairs are established. |
| title | Optimal Control of Two-Phase Membrane Problem |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2405.10704 |