A singularly perturbed problem of chemical kinetics
type: Item
instance of: scholarly article
title: A singularly perturbed problem of chemical kinetics
zbMATH Open document ID: 0547.35011
author: A. B. Vasil'eva
author: O. N. Gorshkova
published in: Moscow University Computational Mathematics and Cybernetics
publication date: 1984-01-01T00:00:00Z
review text: The authors study the initial-boundary value problems \(\partial u^ I/\partial t=\mu^ 2_ 1\partial^ 2u^ I/\partial x^ 2_ 1\), \(u^ I(x_ 1,0)=0,\quad\partial u^ I/\partial x_ 1(0,t)=0;\quad\partial u^{II}/\partial t=\mu^ 2_ 2\partial^ 2u^{II}/\partial x^ 2_ 2,\quad u^{II}(x_ 2,0)=1,\quad\partial u^{II}/\partial x_ 2(0,t)=0,\) which are coupled through the interface conditions \(u^ I(\ell,t)=u^{II}(\ell,t)\) and \([a_ 1\partial u^ I/\partial x_ 1+a_ 2\partial u^{II}/\partial x_ 2+a_ 3u^ I+a_ 4u^{II}+a_ 5](\ell,t)=0,\) in the case when \(\mu_ 1,\mu_ 2\) and \(\mu_ 1/\mu_ 2\) are small. Using asymptotic analysis they are able to prove the existence of a solution \(\{u^ I,u^{II}\}\) and to construct a uniformly valid expansion for \(\{u^ I,u^{II}\}\) that features layer behavior in a neighborhood of \(x=\ell\).
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 3871851
zbMATH Keywords: chemical kinetics
zbMATH Keywords: singular perturbation
zbMATH Keywords: initial-boundary value problems
zbMATH Keywords: interface conditions
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: existence
MaRDI profile type: Publication
Recommended article: Q4527853
Recommended article: Q5194305
Recommended article: Q3979395
Recommended article: Q3363753
Recommended article: Singular perturbation for a class of coupled chemical reaction and diffusion systems
Recommended article: Singularly Perturbed Problems Modeling Reaction-convection-diffusion Processes
Recommended article: Q4549115
Recommended article: Periodic solution to a kind of singularly perturbed differential equations of parabolic type in chemical kinetics
Recommended article: An identification problem for singular systems with a small parameter in chemical kinetics
Recommended article: Q4809878
description: scientific article; zbMATH DE number 3871851