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<p>The purpose of this paper is to prove the existence and uniqueness of bounded weak solutions for a doubly nonlinear parabolic problem of <i>p</i>-Laplacian type with a nonlinear boundary condition. We formulate our problem as a dynamical system; then by using Hölder continuity of solutions and assuming appropriate hypotheses, we prove also the existence of a global attractor in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2024_2349_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{\infty }(\Omega )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mi>∞</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Global Attractor for a Doubly Nonlinear Parabolic Problem with a Nonlinear Boundary Condition

  • 期刊论文

  • 发表日期：

    2025年1月16日

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  • A. El Hachimi,
  • S. Maatouk

摘要

The purpose of this paper is to prove the existence and uniqueness of bounded weak solutions for a doubly nonlinear parabolic problem of p-Laplacian type with a nonlinear boundary condition. We formulate our problem as a dynamical system; then by using Hölder continuity of solutions and assuming appropriate hypotheses, we prove also the existence of a global attractor in \(L^{\infty }(\Omega )\) L ∞ ( Ω ) .