Rate of convergence of attractors for semilinear singularly perturbed problems: scalar parabolic equations with localized large diffusion

2016/06/12 by Leonardo Martins Pires, Pires, Leonardo, Alexandre N. Carvalho +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1606.03771

openalex publication_date 2016/06/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we study the asymptotic nonlinear dynamics of scalar semilinear parabolic problems reaction-diffusion type when the diffusion coefficient becomes large in a subregion which is interior to the domain. We obtain, under suitable assumptions, that the family of attractors behaves continuously and we exhibit the rate of convergence. An accurate description of localized large diffusion is necessary.

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