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The Initial Boundary Value Problems for Hyperbolic Conservation Laws with Relaxation

Authors
Journal
Journal of Differential Equations
0022-0396
Publisher
Elsevier
Publication Date
Volume
130
Issue
1
Identifiers
DOI: 10.1006/jdeq.1996.0134

Abstract

Abstract The hyperbolic conservation laws with relaxation appear in many physical models such as those for gas dynamics with thermo-non-equilibrium, elasticity with memory, flood flow with friction, traffic flow, etc.. The main concern of this article is the long-time effect of the relaxations on the boundary layer behaviors. In this article, we investigate this problem for a simple model of 2×2 systems. Conditions relating the boundary data and far field states are found for the existence of the boundary layers. Also, it is proven that the boundary layers thus obtained are nonlinearly stable.

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