Linear and nonlinear exponential stability of traveling waves for hyperbolic systems with relaxation

This paper is concerned with the linear and nonlinear exponential stability of traveling wave solutions for a system of quasi-linear hyperbolic equations with relaxation. By applying C0-semigroup theory and detailed spectral analysis, we prove the linear exponential stability of the traveling waves for the quasilinear systems and nonlinear exponential stability of the waves for semi-linear systems, i.e., the Jin-Xin relaxation models, in some exponentially weighted spaces without assuming that the wave strengths are small.

Keywords

Exponential stability, traveling waves, quasi-linear hyperbolic systems, Jin-Xin relaxation models, spectral analysis, weighted spaces

2010 Mathematics Subject Classification

35B30, 35B40, 35L65, 76L05, 90B20

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Published 1 January 2009