Optimal Control of Two-Phase Membrane Problem

IF 1.7 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-06-28 DOI:10.1007/s00245-025-10282-2

Farid Bozorgnia, Vyacheslav Kungurtsev

引用次数: 0

Abstract

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.

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两相膜问题的最优控制

我们考虑一个最优控制问题，其中状态由一个称为两相膜问题的自由边界问题控制，并且控制出现在状态方程的系数中，影响解的正相和负相。我们的研究重点是与控制到状态映射相关的各种属性。由于这个映射的不可微性，我们正则化了状态方程。建立了最优对的存在性、唯一性和性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.