Traveling fronts for the thermo-diffusive system with arbitrary Lewis numbers
type: Item
instance of: scholarly article
title: Traveling fronts for the thermo-diffusive system with arbitrary Lewis numbers
zbMATH Open document ID: 1200.35044
author: François Hamel
author: Lenya Ryzhik
published in: Archive for Rational Mechanics and Analysis
publication date: 2010-07-06T00:00:00Z
review text: The paper deals with a reaction-diffusion system of a special type, namely, of so-called KPP type. The definition domain of the system is cylindrical. The right hand side of the system contains a Lewis number, which is the ratio of thermal and material diffusivities. The main goal of the work is to show that traveling fronts solutions exist for all Lewis numbers and approach uniform limits at the two ends of the cylinder. To substantiate this result, the authors construct the KPP traveling wave using the standard procedure of restricting the problem to a finite cylinder and then passing to the limit of an infinite cylinder. The presumed absence of cellular instabilities in the KPP case makes the proof work from the physical point of view.
reviewed by: Vyacheslav I. Maksimov
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 76V05
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 5731003
zbMATH Keywords: reaction-diffusion equation
zbMATH Keywords: KPP-type system
zbMATH Keywords: Lewis number
zbMATH Keywords: cylindrical domain
MaRDI profile type: Publication
full work available at URL: s00205-009-0234-9
OpenAlex ID: W1975963982
cites work: Front propagation in periodic excitable media
cites work: Quenching and propagation in KPP reaction-diffusion equations with a heat loss
cites work: Traveling Wave Solutions to Combustion Models and Their Singular Limits
cites work: On the method of moving planes and the sliding method
cites work: Travelling fronts in cylinders
cites work: The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form travelling waves
cites work: Non-uniqueness for flame propagation when the Lewis number is less than 1
cites work: On the stability of multiple steady planar flames when the Lewis number is less than 1
cites work: Q4351900
cites work: Multi-dimensional combustion waves for Lewis number close to one
cites work: Two-dimensional travelling wave solutions of a system modelling near equidiffusional flames
cites work: Bifurcations of travelling waves in the thermo-diffusive model for flame propagation
cites work: Non-adiabatic KPP fronts with an arbitrary Lewis number
cites work: Qualitative properties of a nonlinear system for laminar flames without ignition temperature
cites work: Oscillating wave fronts in isothermal chemical systems with arbitrary powers of autocatalysis
cites work: Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
DOI: 10.1007/S00205-009-0234-9
description: scientific article; zbMATH DE number 5731003