Time-asymptotic limit of solutions of a combustion problem
type: Item
instance of: scholarly article
title: Time-asymptotic limit of solutions of a combustion problem
zbMATH Open document ID: 0920.35026
DOI: 10.1023/A:1022629125232
author: Tong Li
published in: Journal of Dynamics and Differential Equations
publication date: 1999-09-01T00:00:00Z
review text: From author's summary: A combustion model which captures the interacting among nonlinear convection, chemical reaction and radiative heat transfer is studied. New phenomena are found with radiative heat transfer present. In particular, there is a detonation wave solution in which there is a sonic point inside the reaction zone. As a consequence, the traveling wave speed cannot be determined before the problem is solved. The shooting method is used to prove the existence of the traveling wave. The condition we shoot at is the compatibility condition at the sonic point. Furthermore, the speed of the detonation wave decreases as the heat loss coefficient increases, as expected physically. We study the time-asymptotic limit of solutions of the initial value problem for the same problem. We prove that the solution exists globally and the solution converges uniformly, away from the shock, to a shifted traveling wave solution as \(t\to+\infty\) for certain ``compact support'' initial data.
reviewed by: Knut Smoczyk
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35L67
zbMATH DE Number: 1234929
zbMATH Keywords: detonation
zbMATH Keywords: radiation effect
zbMATH Keywords: shock wave
zbMATH Keywords: sonic point
zbMATH Keywords: the shooting method
zbMATH Keywords: traveling wave speed
MaRDI profile type: Publication
full work available at URL: a:1022629125232
OpenAlex ID: W1533086848
description: scientific article; zbMATH DE number 1234929