晶界运动PDE模型控制的约束优化问题

IF 3.2 1区数学 Q1 MATHEMATICS

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI:10.1515/anona-2022-0242

Harbir Antil, Shodai Kubota, K. Shirakawa, N. Yamazaki

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引用次数: 0

摘要

摘要本文考虑一类由Kobayashi Warren Carter型状态方程控制的最优控制问题。控制是由物理温度决定的。重点是维度小于或等于4的问题。结果分为四个主要定理：状态方程和最优控制问题的可解性和参数依赖性；这些正则化最优控制问题的一阶必要最优性条件。随后，我们推导了极限系统和最优性条件，并研究了它们的适定性。

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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Constrained optimization problems governed by PDE models of grain boundary motions

Abstract In this article, we consider a class of optimal control problems governed by state equations of Kobayashi-Warren-Carter-type. The control is given by physical temperature. The focus is on problems in dimensions less than or equal to 4. The results are divided into four Main Theorems, concerned with: solvability and parameter dependence of state equations and optimal control problems; the first-order necessary optimality conditions for these regularized optimal control problems. Subsequently, we derive the limiting systems and optimality conditions and study their well-posedness.

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来源期刊

Advances in Nonlinear Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

6.00

自引率

9.50%

发文量

审稿时长

30 weeks

期刊介绍： Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The Journal focuses on papers that address significant problems in pure and applied nonlinear analysis. ANONA seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.