Asymptotic behaviour and source-type solutions for a diffusion-convection equation
type: Item
instance of: scholarly article
title: Asymptotic behaviour and source-type solutions for a diffusion-convection equation
zbMATH Open document ID: 0807.35059
DOI: 10.1007/BF00392203
author: M. Escobedo
author: Juan Luis Vázquez
author: Enrique Zuazua
published in: Archive for Rational Mechanics and Analysis
publication date: 1995-03-09T00:00:00Z
review text: The paper deals with the equation \(u_ t = u_{xx} - | u |^{q - 1} u_ x\), \(t > 0\), \(x \in \mathbb{R}\). The asymptotic behaviour of the solutions of this equation is studied in the subcritical exponent range, that is, in the case \(1<q<2\). It is proved that as \(t \to \infty\) the solutions with integrable data look like the entropy solutions of the equation \(u_ t + (| u |^{q - 1} u/q)_ x = 0\) with initial data \(M \delta (x)\). Also the authors investigate the question of existence of fundamental solutions of the equation under consideration and they construct fundamental solutions for all exponents \(q>1\).
reviewed by: Emil Minchev
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35E05
zbMATH DE Number: 474500
zbMATH Keywords: source-type solutions
zbMATH Keywords: diffusion-convection equation
zbMATH Keywords: subcritical exponent range
zbMATH Keywords: entropy solutions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00392203
OpenAlex ID: W2054856063
description: scientific article; zbMATH DE number 474500