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<p>In this paper, we study the long-time behavior of the semigroup&#xa0;<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2002_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>S</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$S(t)$</EquationSource> </InlineEquation>&#xa0;generated by a nonlinear viscoelastic equation with strong damping in a bounded domain&#xa0;Ω&#xa0;of&#xa0;<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2002_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="double-struck">R</mi> <mi>N</mi> </msup> </math></EquationSource> <EquationSource Format="TEX">$\mathbb{R}^{N}$</EquationSource> </InlineEquation>.&#xa0;We prove the well-posedness and the existence of the global attractor associated to this problem.</p>

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Global attractors for a nonlinear viscoelastic equations with strong damping velocity-dependent material density

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  • 发表日期：

    2025年6月12日

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  • Suli Zhang

摘要

In this paper, we study the long-time behavior of the semigroup  S ( t ) $S(t)$  generated by a nonlinear viscoelastic equation with strong damping in a bounded domain Ω of  R N $\mathbb{R}^{N}$ . We prove the well-posedness and the existence of the global attractor associated to this problem.