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Spatial homogeneity in parabolic problems with nonlinear boundary conditions

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  • In this work we prove that global attractors of systems of weakly coupled parabolic equations with nonlinear boundary conditions and large diffusivity are close to attractors of an ordinary differential equation. The limiting ordinary differential equation is given explicitly in terms of the reaction, boundary flux, the $n$-dimensional Lebesgue measure of the domain and the $(n-1)-$Hausdorff measure of its boundary. The tools are invariant manifold theory and comparison results.
    Mathematics Subject Classification: 34D35, 34D45, 35B05, 35B40, 35K40.

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