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<p>A system of two double nonlinear diffusion equations acting on two different rectangles in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb {R}}^2,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> connected by the nonlinear boundary conditions on the contact line, is studied. We prove the existence and uniqueness of a weak solution. Moreover, we illustrate the solution using numerical scheme based on finite volume discretization in space and explicit time discretization. The paper is an extension of previous results of Filo and Pluschke, who dealt with a system of two porous medium equations defined on two different components of the real line connected by a nonlinear contact condition.</p>

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Double nonlinear diffusion equations in a two-component domain

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月18日

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  • Jela Babušíková,
  • Ján Filo,
  • Patrik Mihala

摘要

A system of two double nonlinear diffusion equations acting on two different rectangles in \({\mathbb {R}}^2,\) R 2 , connected by the nonlinear boundary conditions on the contact line, is studied. We prove the existence and uniqueness of a weak solution. Moreover, we illustrate the solution using numerical scheme based on finite volume discretization in space and explicit time discretization. The paper is an extension of previous results of Filo and Pluschke, who dealt with a system of two porous medium equations defined on two different components of the real line connected by a nonlinear contact condition.