A Representation Formula for Viscosity Solutions of Nonlocal Hamilton–Jacobi Equations and Applications

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-03 DOI:10.1137/23m1608136

Takashi Kagaya, Qing Liu, Hiroyoshi Mitake

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 5807-5839, October 2024.
Abstract. This paper is concerned with geometric motion of a closed surface whose velocity depends on a nonlocal quantity of the enclosed region. Using the level set formulation, we study a class of nonlocal Hamilton–Jacobi equations and establish a control-based representation formula for solutions. We also apply the formula to discuss the fattening phenomenon and large-time asymptotics of the solutions.

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非局部汉密尔顿-雅可比方程粘度解的表示公式及其应用

SIAM 数学分析期刊》，第 56 卷第 5 期，第 5807-5839 页，2024 年 10 月。摘要本文关注速度取决于封闭区域非局部量的封闭表面的几何运动。利用水平集公式，我们研究了一类非局部汉密尔顿-雅可比方程，并建立了基于控制的解表示公式。我们还应用该公式讨论了解的肥大现象和大时间渐近性。

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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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.