Constrained optimization problems governed by PDE models of grain boundary motions-Reference-Cited by-同舟云学术

Constrained optimization problems governed by PDE models of grain boundary motions

Published:2022-01-01 Issue:1 Volume:11 Page:1249-1286
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Antil Harbir¹,Kubota Shodai²,Shirakawa Ken³,Yamazaki Noriaki⁴

Affiliation:

1. Department of Mathematical Sciences and the Center for Mathematics and Artificial Intelligence, (CMAI), George Mason University , Fairfax , VA 22030 , USA

2. Department of Mathematics and Informatics, Graduate School of Science and Engineering, Chiba University , 1–33, Yayoi-cho , Inage-ku , 263-8522, Chiba , Japan

3. Department of Mathematics, Faculty of Education, Chiba University, 1-33, Yayoi-cho , Inage-ku , 263-8522, Chiba , Japan

4. Department of Mathematics, Faculty of Engineering, Kanagawa University, 3–27–1, Rokkakubashi, Kanagawa-ku , Yokohama , 221–8686 , Japan

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anona-2022-0242/pdf

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