Limit of solutions for semilinear Hamilton–Jacobi equations with degenerate viscosity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-05-16 DOI:10.1515/acv-2022-0108

Jian-lin Zhang

引用次数: 1

Abstract

Abstract In the paper we prove the convergence of viscosity solutions u λ {u_{\lambda}} as λ → 0 + {\lambda\rightarrow 0_{+}} for the parametrized degenerate viscous Hamilton–Jacobi equation H ⁢ ( x , d x ⁢ u , λ ⁢ u ) = α ⁢ ( x ) ⁢ Δ ⁢ u , α ⁢ ( x ) ≥ 0 , x ∈ 𝕋 n H(x,d_{x}u,\lambda u)=\alpha(x)\Delta u,\quad\alpha(x)\geq 0,\quad x\in\mathbb% {T}^{n} under suitable convex and monotonic conditions on H : T * ⁢ M × ℝ → ℝ {H:T^{*}M\times\mathbb{R}\rightarrow\mathbb{R}} . Such a limit can be characterized in terms of stochastic Mather measures associated with the critical equation H ⁢ ( x , d x ⁢ u , 0 ) = α ⁢ ( x ) ⁢ Δ ⁢ u . H(x,d_{x}u,0)=\alpha(x)\Delta u.

查看原文本刊更多论文

退化粘性的双线性Hamilton–Jacobi方程解的极限

摘要本文证明了黏性解u λ的收敛性 {我们……{\lambda}} 当λ→0 + {\lambda\rightarrow 0＿{+}} 对于参数化简并粘性Hamilton-Jacobi方程H∑(x,d x∑u， λ∑u) = α∑(x)∑Δ∑u， α∑(x)≥0,x∈ndh (x,d＿{x}你，\lambda u)=\alpha(x)\Delta 你，\quad\alpha(x)\geq 0，\quad x\in\mathbb% {T}^{n} under suitable convex and monotonic conditions on H : T * ⁢ M × ℝ → ℝ {H:T^{*}M\times\mathbb{R}\rightarrow\mathbb{R}} . Such a limit can be characterized in terms of stochastic Mather measures associated with the critical equation H ⁢ ( x , d x ⁢ u , 0 ) = α ⁢ ( x ) ⁢ Δ ⁢ u . H(x,d_{x}u,0)=\alpha(x)\Delta u.

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.