Initial boundary value problem for the system of compressible adiabatic flow through porous media
type: Item
instance of: scholarly article
title: Initial boundary value problem for the system of compressible adiabatic flow through porous media
zbMATH Open document ID: 0942.35138
author: Ling Hsiao
author: Ronghua Pan
published in: Journal of Differential Equations
publication date: 2000-03-02T00:00:00Z
review text: The authors study the initial value problem for the system of compressible adiabatic flow through porous media in one space dimension with fixed boundary conditions. The global existence and uniqueness for the classical solution are obtained and the exponential convergence to a stationary state is established. Estimates of the solution are derived under restrictions concerning the oscillations in the initial data. It is also shown that the problem can be approximated very well time-asymptotically by an initial boundary problem for the related diffusion equations obtained from the original hyperbolic system by Darcy's law, provided that the initial total mass is the same. The difference between these two solutions tends to zero exponentially fast as time goes to infinity. The diffusive phenomena caused by damping mechanism with boundary effects are thus observed.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 1389124
zbMATH Keywords: stationary state
zbMATH Keywords: oscillations in the initial data
zbMATH Keywords: hyperbolic system
zbMATH Keywords: Darcy's law
zbMATH Keywords: diffusion equations
reviewed by: Adrian Carabineanu
MaRDI profile type: Publication
OpenAlex ID: W2108954855
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DOI: 10.1006/JDEQ.1999.3648
description: scientific article; zbMATH DE number 1389124