Travelling wave solutions in a model for filtration combustion
type: Item
instance of: scholarly article
title: Travelling wave solutions in a model for filtration combustion
zbMATH Open document ID: 1078.34025
author: Fathi Dkhil
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-09-23T00:00:00Z
review text: The existence and uniqueness of travelling wave solutions of the evolution system \[ \gamma\widehat\theta_t-(\gamma-1)\widehat\Pi_t= \Omega(\widehat\varphi,\widehat\theta),\quad \widehat\varphi_t=-\Omega(\widehat\varphi,\widehat\theta), \quad \widehat\Pi_t- \widehat\theta_t= \widehat\Pi_{xx}, \] for \(x\in\mathbb{R}\) and \(t>0\), are proved. This system arises in a combustion model proposed by [\textit{I.~Brailovsky, M.~Frankel} and \textit{G. I.~Sivashinsky} [Combust. Theory Model 4, 47--60 (2000; Zbl 0966.76098)]. The variables are here the temperature \(\widehat\theta(x,t)\), the pressure \(\widehat\Pi(x,t)\) and the concentration of the deficient reactant \(\widehat\varphi(x,t)\). The term \(\Omega(\widehat\varphi,\widehat\theta)\) is the nonlinear reaction term and the constant \(\gamma>1\) only depends on the reacting mixture. The author is interested in travelling wave solutions to this system of the form \(\widehat\theta(x,t)=\theta(x+ct)\), \(\widehat\Pi(x,t)=\Pi(x+ct)\), \(\widehat\varphi(x,t)=\varphi(x+ct)\), where the number \(c\) is proportional to the propagation speed of the combustion front. An estimate of the wave speed is established, too.
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 35K99
Mathematics Subject Classification ID: 34B40
zbMATH DE Number: 2102592
zbMATH Keywords: combustion
zbMATH Keywords: deflagration
zbMATH Keywords: travelling fronts
zbMATH Keywords: reaction-diffusion
reviewed by: Victor S. Rykhlov
MaRDI profile type: Publication
full work available at URL: j.na.2004.01.005
OpenAlex ID: W1987313248
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DOI: 10.1016/J.NA.2004.01.005
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description: scientific article; zbMATH DE number 2102592