A semilinear reaction-diffusion system of equations and large diffusion
type: Item
instance of: scholarly article
title: A semilinear reaction-diffusion system of equations and large diffusion
zbMATH Open document ID: 1065.35071
author: Robert Willie
published in: Journal of Dynamics and Differential Equations
publication date: 2005-01-17T00:00:00Z
review text: The author deals with the following semilinear system of reaction and diffusion equations \[ \left.\begin{aligned} \partial_t u-\text{Div}(D^\varepsilon \nabla u)+V^\varepsilon u+\lambda u=f(u)\qquad & \text{in }\Omega,\;t>0\\ \partial_nu+B^\varepsilon u=g(u)\qquad & \text{on }\Gamma\\ u(0)=u^\varepsilon_0\qquad & \text{in }\Omega\end{aligned}\right\}\tag{1} \] with nonlinear flux. The author studies the natural limit of the solutions (1) for large diffusivity. To this end, the author first shows the existence of a global attractor \({\mathcal A}^\varepsilon\) and proves that the flow on the family of attractors \({\mathcal A}^\varepsilon\) are essentially close to one generated by ODEs, which is a natural limit process for large diffusivity.
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 2128700
zbMATH Keywords: invariant manifold
zbMATH Keywords: global attractor
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
DOI: 10.1023/B:JODY.0000041280.69325.A4
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description: scientific article; zbMATH DE number 2128700