\(L^ p\) asymptotic behavior of solutions to hyperbolic-parabolic systems of conservation laws
type: Item
instance of: scholarly article
title: \(L^ p\) asymptotic behavior of solutions to hyperbolic-parabolic systems of conservation laws
zbMATH Open document ID: 0858.35050
DOI: 10.1007/BF01207832
author: Yanni Zeng
published in: Archiv der Mathematik
publication date: 1996-10-27T00:00:00Z
review text: We study the large time behavior in \(L^p\) of solutions to a general \(n\times n\) hyperbolic-parabolic system of conservation laws. Under physical assumptions on the dissipativeness of the system, we show that the solution to the Cauchy problem is approximated by the solution to a uniformly parabolic system when the initial data are smooth and small. In turn the solution of the hyperbolic-parabolic system is approximated by a superposition of linear and nonlinear diffusion waves, self-similar solutions of the heat equation and the Burgers equation. The \(L^p\) \((1\leq p\leq\infty)\) optimal convergence rates are obtained. The approach is based on the pointwise estimates in the physical space of the Green's function of the linearized system. Our result applies to the compressible Navier-Stokes equations.
reviewed by: Zeng Yuesheng
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 938541
zbMATH Keywords: hyperbolic-parabolic system of conservation laws
zbMATH Keywords: nonlinear diffusion waves
zbMATH Keywords: self-similar solutions
zbMATH Keywords: Burgers equation
zbMATH Keywords: compressible Navier-Stokes equations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 938541