时空相场断裂互补模型及其优化控制公式分析

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-05 DOI:10.1137/23m1605314

Denis Khimin, Johannes Lankeit, Marc C. Steinbach, Thomas Wick

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引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷第 5 期，第 6192-6212 页，2024 年 10 月。摘要这项工作的目的是提出相场最优控制问题的最优性条件。首先将前向问题表述为一个抽象的非线性优化问题，然后推导出必要的最优性条件。同时还研究了充分最优条件。如何选择合适的函数空间来确保非线性优化问题的正则性是一个真正的挑战。随后，我们提出了具有跟踪型成本函数的最优控制问题。约束条件由之前得出的前向问题一阶最优条件给出。在这里，正则性在某些条件下得到了证明，并提出了一阶最优条件。

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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Analysis of a Space-Time Phase-Field Fracture Complementarity Model and its Optimal Control Formulation

SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 6192-6212, October 2024.
Abstract. The purpose of this work is the formulation of optimality conditions for phase-field optimal control problems. The forward problem is first stated as an abstract nonlinear optimization problem, and then the necessary optimality conditions are derived. The sufficient optimality conditions are also examined. The choice of suitable function spaces to ensure the regularity of the nonlinear optimization problem is a true challenge here. Afterwards the optimal control problem with a tracking type cost functional is formulated. The constraints are given by the previously derived first order optimality conditions of the forward problem. Herein regularity is proven under certain conditions and first order optimality conditions are formulated.

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.