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<p>This paper considers a model of a reaction-diffusion equation with large diffusion and convection heating at the boundary, which consists of a family of coupled PDE-ODE systems with nonhomogeneous boundary conditions. We analyze the singular limiting problem by examining the convergence of linear and nonlinear problems. We apply the Invariant Manifold Theorem to reduce the problem to finite dimensions and prove the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12591_2024_705_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> convergence of the solutions. Conditions to ensure the structural stability of the system are also derived.</p>

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Reaction-Diffusion Equations with Large Diffusion and Convection Heating at the Boundary

  • 期刊论文

  • 发表日期：

    2025年1月5日

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  • Leonardo Pires

摘要

This paper considers a model of a reaction-diffusion equation with large diffusion and convection heating at the boundary, which consists of a family of coupled PDE-ODE systems with nonhomogeneous boundary conditions. We analyze the singular limiting problem by examining the convergence of linear and nonlinear problems. We apply the Invariant Manifold Theorem to reduce the problem to finite dimensions and prove the \(C^1\) C 1 convergence of the solutions. Conditions to ensure the structural stability of the system are also derived.