Weak solutions of a conservation law with memory in several space variables
type: Item
instance of: scholarly article
title: Weak solutions of a conservation law with memory in several space variables
zbMATH Open document ID: 0897.35050
author: Rosella Sampalmieri
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 1998-02-11T00:00:00Z
review text: The author establishes the existence and uniqueness of the weak solution of a Cauchy problem associated to a conservation law in several space variables, whose non-homogeneous term is a ``memory'' term. The existence is obtained, in a particular case, by proving the uniform boundedness of the approximate solutions in the BV-norm, and then applying the relative compactness framework, in the general case, in the \(L^1\)-framework. The uniqueness is obtained by means of a suitable modification of Kruzkov's method.
reviewed by: Jinghua Wang
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 1117670
zbMATH Keywords: relative compactness
MaRDI profile type: Publication
full work available at URL: s000300050036
OpenAlex ID: W1971535869
DOI: 10.1007/S000300050036
description: scientific article; zbMATH DE number 1117670