Contrast structures: Theory and applications
type: Item
instance of: scholarly article
title: Contrast structures: Theory and applications
zbMATH Open document ID: 0904.35007
DOI: 10.1007/BF01128943
author: V. F. Butuzov
author: A. B. Vasil'eva
author: N. N. Nefedov
published in: Computational Mathematics and Modeling
publication date: 1998-08-25T00:00:00Z
review text: A number of important applied problems in chemical kinetics, synergetics, biology, astrophysics, and semiconductor physics lead to reaction-diffusion-advection equations. In many cases (fast reactions, small diffusion, etc.) these equations are singularly perturbed, and their solutions therefore have zones characterized by fast spatial-temporal variation (boundary and interior layers). The most difficult case to study is when the solution undergoes fast changes in the interior of the domain. Such solutions will be called contrast structures. We qualitatively classify these contrast structures into two groups: bursts and steps. Numerical solution of such problems is quite difficult, and it must allow for the qualitative behavior of the solution, information about which is supplied by the asymptotic solution of the problem. In this paper, we present the main directions and results for research into the asymptotic theory of contrast structures carried out at the Department of Mathematics of the Faculty of Physics at the Moscow State University. The main topics include: existence and evolution of contrast structures, stability analysis of contrast structures, and contrast structures in applied problems.
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1188590
zbMATH Keywords: stationary reaction-diffusion equation
zbMATH Keywords: boundary and interior layers
zbMATH Keywords: reaction-diffusion-advection equations
zbMATH Keywords: contrast structures
zbMATH Keywords: bursts
zbMATH Keywords: steps
zbMATH Keywords: asymptotic theory
zbMATH Keywords: stability
MaRDI profile type: Publication
cites work: Q3573541
full work available at URL: https://doi.org/10.1007/bf01128943
OpenAlex ID: W1984469497
description: scientific article; zbMATH DE number 1188590