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Abstract <p>The global attractors of nonclassical diffusion equations in Orlicz spaces without upper growth restriction on nonlinearity are investigated in this work. The well-posedness of solutions for equations in Orlicz spaces is demonstrated. In addition, the existence of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7224_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="113" /> </InlineMediaObject> <EquationSource Format="TEX">\((\mathcal{L}^{2}(\Upsilon),\mathcal{L}^{\infty}(\Upsilon))\)</EquationSource> <!--ContMath2460146Youssouf-m3--> </InlineEquation>-bounded absorbing sets is proven. Finally, we show the asymptotic compactness of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7224_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="75" /> </InlineMediaObject> <EquationSource Format="TEX">\(\{S(\vartheta)\}_{\vartheta\geq 0}\)</EquationSource> <!--ContMath2460146Youssouf-m4--> </InlineEquation> associated with the problem and then obtain the existence of global attractors in a given Orlicz space.</p>

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Global Attractors of Nonclassical Diffusion Equations in Orlicz Spaces \(\boldsymbol{\mathcal{L}}^{\boldsymbol{\ast}}_{\boldsymbol{\mathcal{K}}}{(\Upsilon)}\)

  • 期刊论文

  • 发表日期：

    2025年6月27日

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  • Abdoulaye Ali Youssouf,
  • Qiaozhen Ma,
  • Wenhui Ma,
  • Chang Zhang

摘要

Abstract

The global attractors of nonclassical diffusion equations in Orlicz spaces without upper growth restriction on nonlinearity are investigated in this work. The well-posedness of solutions for equations in Orlicz spaces is demonstrated. In addition, the existence of \((\mathcal{L}^{2}(\Upsilon),\mathcal{L}^{\infty}(\Upsilon))\) -bounded absorbing sets is proven. Finally, we show the asymptotic compactness of \(\{S(\vartheta)\}_{\vartheta\geq 0}\) associated with the problem and then obtain the existence of global attractors in a given Orlicz space.