具有非局部项的p-Laplace方程的边界最优控制
Boundary Optimal Control of the p-Laplace Equation with Non-Local Terms
DOI: 10.12677/pm.2024.1410344, PDF,    国家自然科学基金支持
作者: 刘彩芳：兰州交通大学数理学院，甘肃 兰州
关键词: p-Laplace方程；解的存在唯一性；边界控制；p-Laplace Equation； Existence and Uniqueness of Solutions； Boundary Control
摘要: 本文研究了一类具有非局部项的p-Laplace方程的边界最优控制问题，通过对成本泛函的极小化序列取极限给出p-Laplace方程初边值问题最优控制函数的存在性。首先利用能量估计方法研究该问题解的存在唯一性，其次利用紧性估计和紧嵌入定理分析成本泛函极小化序列的收敛性，最后由成本泛函的弱下半连续性证明最优控制函数的存在性。
Abstract: In this paper, we study the boundary optimal control problem of a class of p-Laplace equations with non-local terms, and the existence of the optimal control function of the initial boundary value problem of the p-Laplace equation is given by taking the limit of the minimization sequence of the cost function. Firstly, the energy estimation method is used to study the existence uniqueness of the solution of the problem, then the tightness estimation and the tight embedding theorem are used to analyze the convergence of the cost functional minimization sequence, and finally the existence of the optimal control function is proved by the weak lower semi-continuity of the cost function.
文章引用：刘彩芳. 具有非局部项的p-Laplace方程的边界最优控制[J]. 理论数学, 2024, 14(10): 55-65. https://doi.org/10.12677/pm.2024.1410344

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