A singularly perturbed ``reaction-diffusion-transfer'' system which degenerates into a system with a finite equation and a first-order partial differential equation
type: Item
instance of: scholarly article
title: A singularly perturbed ``reaction-diffusion-transfer'' system which degenerates into a system with a finite equation and a first-order partial differential equation
zbMATH Open document ID: 0848.35007
author: V. F. Butuzov
author: S. T. Esimova
published in: Computational Mathematics and Mathematical Physics
publication date: 1996-05-28T00:00:00Z
review text: We consider the homogeneous Neumann boundary value problem for the following singularly perturbed semilinear parabolic system: \[ \left. \begin{aligned} \varepsilon {\partial u\over \partial t} & + \varepsilon b(x) {\partial u\over \partial x}- \varepsilon^3 a_1(x) {\partial^2 u\over \partial x^2}= f(u, v, x, t)\\ {\partial v\over \partial t} & + b(x) {\partial v\over \partial x}- \varepsilon^2 a_2(x) {\partial^2 v\over \partial x^2}= g(u, v, x, t)\end{aligned} \right\}\quad 0< x< 1, \] where \(\varepsilon> 0\) is a small parameter. We construct an asymptotic approximation for small values of \(\varepsilon\) for the solution up to the order \(\varepsilon^2\). The arrangement of the small parameter \(\varepsilon\) corresponds to slow diffusion in both equations, fast reactions in the first equation (the reaction rate is of order \(\varepsilon^{-1}\)) and slow reactions in the second equation.
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 859640
zbMATH Keywords: homogeneous Neumann boundary value problem
zbMATH Keywords: semilinear parabolic system
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 859640