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Stability of travelling wave solutions to a semilinear hyperbolic system with relaxation

✍ Scribed by Yoshihiro Ueda

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
144 KB
Volume
32
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We study a semilinear hyperbolic system with relaxation and investigate the asymptotic stability of travelling wave solutions with shock profile. It is shown that the travelling wave solution is asymptotically stable, provided the initial disturbance is suitably small. Moreover, we show that the time convergence rate is polynomially (resp. exponentially) fast as tβ†’βˆž if the initial disturbance decays polynomially (resp. exponentially) for xβ†’βˆž. Our proofs are based on the space–time weighted energy method. Copyright Β© 2008 John Wiley & Sons, Ltd.

πŸ“œ SIMILAR VOLUMES

Global solutions with shock waves to the
Global solutions with shock waves to the generalized Riemann problem for a class of quasilinear hyperbolic systems of balance laws II
✍ Zhi-Qiang Shao πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 265 KB πŸ‘ 1 views

## Abstract This work is a continuation of our previous work. In the present paper, we study the existence and uniqueness of global piecewise __C__^1^ solutions with shock waves to the generalized Riemann problem for general quasilinear hyperbolic systems of conservation laws with linear damping in