Scholarlink

<p>In this paper, the limiting behavior of invariant measures is mainly investigated for a class of stochastic quasilinear parabolic equations with nonlinear noise on thin domains. The existence and uniqueness of invariant measure on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10311_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\((n+1)\)</EquationSource> </InlineEquation>-dimensional thin domains are presented. The difficulty on estimates of the solutions for such problems in Sobolev space in the sense of thin domains is overcome by a novel proof techniques. Hence, the research results reveal that any limit of invariant measures of original equations on thin domains must be an invariant measure of the limiting equations when the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10311_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\((n+1)\)</EquationSource> </InlineEquation>-dimensional thin domains degenerates onto the <i>n</i>-dimensional space.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Limiting Behavior of Invariant Measures for Stochastic Quasilinear Parabolic Equations with Nonlinear Noise on Thin Domains

  • 期刊论文

  • 发表日期：

    2025年9月15日

查看全文
  • Zhe Pu,
  • Dingshi Li

摘要

In this paper, the limiting behavior of invariant measures is mainly investigated for a class of stochastic quasilinear parabolic equations with nonlinear noise on thin domains. The existence and uniqueness of invariant measure on \((n+1)\) -dimensional thin domains are presented. The difficulty on estimates of the solutions for such problems in Sobolev space in the sense of thin domains is overcome by a novel proof techniques. Hence, the research results reveal that any limit of invariant measures of original equations on thin domains must be an invariant measure of the limiting equations when the \((n+1)\) -dimensional thin domains degenerates onto the n-dimensional space.