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<p>In this paper, we study a class of nonlinear anisotropic parabolic problems in bounded domains. In detail, we study the influences of the initial data and the forcing term <i>f</i> on the behavior of the solutions. We prove existence and uniqueness results. We indagate on the behavior in time of the solutions with a particular attention to the autonomous case <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="28_2025_1074_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="102" /> </InlineMediaObject> <EquationSource Format="TEX">\(f(x,t)=f(x)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Uniqueness, regularity and behavior in time of the solutions to nonlinear anisotropic parabolic equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月12日

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  • Giuseppina di Blasio,
  • Maria Michaela Porzio

摘要

In this paper, we study a class of nonlinear anisotropic parabolic problems in bounded domains. In detail, we study the influences of the initial data and the forcing term f on the behavior of the solutions. We prove existence and uniqueness results. We indagate on the behavior in time of the solutions with a particular attention to the autonomous case \(f(x,t)=f(x)\) f ( x , t ) = f ( x ) .