Asymptotic profile of solutions of conservation laws with source
type: Item
instance of: scholarly article
title: Asymptotic profile of solutions of conservation laws with source
zbMATH Open document ID: 0851.35090
author: Carlo Sinestrari
published in: Differential and Integral Equations
publication date: 1996-11-18T00:00:00Z
review text: The author investigates the Cauchy problem for the following balance law: \(u_t+ f(u)_x= g(u)\), \(x\in \mathbb{R}\), \(t> 0\), with convex flux \(f\) and initial value with compact support. The source function \(g\in C^1\) is supposed to have a finite number of zeros with \(g(0)= 0\) and to satisfy \(g(v)v\leq \alpha v^2+ \beta\) for some \(\alpha\), \(\beta> 0\). It is proved, that the asymptotic profile of the generalized solution consists in a number of rarefaction waves divided by regions where the solutions oscillate around an unstable zero of the source term.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 856934
zbMATH Keywords: asymptotic profile
zbMATH Keywords: rarefaction waves
reviewed by: Alexandr Doktor
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 856934