Decay of solutions for the equations of isothermal gas dynamics
type: Item
instance of: scholarly article
title: Decay of solutions for the equations of isothermal gas dynamics
zbMATH Open document ID: 0788.35086
DOI: 10.1007/BF03167207
author: Fumioki Asakura
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 1994-06-06T00:00:00Z
review text: The equations of isothermical gas dynamics are expressed by the system \(u_ t+(k^ 2/v)_ x=0\), \(v_ t-u_ x=0\) of nonlinear hyperbolic conservation laws possessing a convex entropy. The author establishes conservation shock waves and rarefaction waves, using some results of Glimm, Nishida, DiPerna and others. He proves the uniformly boundedness of the total amount of wave interaction. The main aim of the paper is the proof of the fact, that the total variation of the solution to the above problem for the initial data having not necessarily small oscillations decays to zero at the rate \(t^{-1/2}\).
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 76N99
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 446765
zbMATH Keywords: equations of isothermical gas dynamics
zbMATH Keywords: nonlinear hyperbolic conservation laws
zbMATH Keywords: convex entropy
zbMATH Keywords: conservation shock waves
zbMATH Keywords: rarefaction waves
zbMATH Keywords: uniformly boundedness of the total amount of wave interaction
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 446765