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<p>This paper concerns quasilinear parabolic equations with p-Laplacian and q-Laplacian–Beltrami principal operators, subject to nonlinear dynamic boundary conditions. We examine the effect of large diffusion on the system, which leads to spatial homogenization. We establish the well-posedness of the perturbed problem and prove that, as the diffusion coefficients become large, the solution converges to that of a limiting system of ordinary differential equations. Additionally, we demonstrate the upper semicontinuity of the attractors, showing their converge to the limiting attractor as the parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation> tends to zero.</p>

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A quasilinear problem with large diffusion and nonlinear dynamic boundary conditions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月10日

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  • Leonardo Pires,
  • Rodrigo A. Samprogna

摘要

This paper concerns quasilinear parabolic equations with p-Laplacian and q-Laplacian–Beltrami principal operators, subject to nonlinear dynamic boundary conditions. We examine the effect of large diffusion on the system, which leads to spatial homogenization. We establish the well-posedness of the perturbed problem and prove that, as the diffusion coefficients become large, the solution converges to that of a limiting system of ordinary differential equations. Additionally, we demonstrate the upper semicontinuity of the attractors, showing their converge to the limiting attractor as the parameter \(\varepsilon \) ε tends to zero.