Communications in Mathematical Sciences
Volume 7 (2009)
Linear and nonlinear exponential stability of traveling waves for hyperbolic systems with relaxation
Pages: 571 – 593
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.
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