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<p>We study homogenization problem for non-autonomous parabolic equations of the form <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13324_2025_1089_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">\(\partial _t u=L(t)u\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>∂</mi> <mi>t</mi> </msub> <mi>u</mi> <mo>=</mo> <mi>L</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mi>u</mi> </mrow> </math></EquationSource> </InlineEquation> with an integral convolution type operator <i>L</i>(<i>t</i>) that has a non-symmetric jump kernel which is periodic in spatial variables and in time. It is assumed that the space-time scaling of the environment is not diffusive. We show that asymptotically the spatial and temporal evolutions of the solutions are getting decoupled, and the homogenization result holds in a moving frame.</p>

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Homogenization of parabolic problems for non-local convolution type operators under non-diffusive scaling of coefficients

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月30日

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  • A. Piatnitski,
  • E. Zhizhina

摘要

We study homogenization problem for non-autonomous parabolic equations of the form \(\partial _t u=L(t)u\) ∂ t u = L ( t ) u with an integral convolution type operator L(t) that has a non-symmetric jump kernel which is periodic in spatial variables and in time. It is assumed that the space-time scaling of the environment is not diffusive. We show that asymptotically the spatial and temporal evolutions of the solutions are getting decoupled, and the homogenization result holds in a moving frame.