Scholarlink

<p>We study the long-time behavior of some Kirchhoff-type wave equation in the space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H_0^1(\Omega )\times L^2(\Omega )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>H</mi> <mn>0</mn> <mn>1</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> <mo>×</mo> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Under the situation where the stiffness coefficient is degenerate at zero, we prove the existence of global attractors when the nonlinearity grows critically, and also the finite-dimensionality of the global attractor when the nonlinearity satisfies the sub-critical growth condition.</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

Finite fractal dimension of global attractors for some Kirchhoff-type wave equations

  • 期刊论文

  • 发表日期：

    2026年2月25日

查看全文
  • Zhijun Tang,
  • Tomás Caraballo,
  • Chengkui Zhong

摘要

We study the long-time behavior of some Kirchhoff-type wave equation in the space \(H_0^1(\Omega )\times L^2(\Omega )\) H 0 1 ( Ω ) × L 2 ( Ω ) . Under the situation where the stiffness coefficient is degenerate at zero, we prove the existence of global attractors when the nonlinearity grows critically, and also the finite-dimensionality of the global attractor when the nonlinearity satisfies the sub-critical growth condition.