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<p>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 state equation, influencing the positive and negative phases 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.</p>

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Optimal Control of Two-Phase Membrane Problem

  • 期刊论文

  • 发表日期：

    2025年6月28日

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  • Farid Bozorgnia,
  • Vyacheslav Kungurtsev

摘要

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 state equation, influencing the positive and negative phases 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.