Stability of traveling waves in quasi-linear hyperbolic systems with relaxation and diffusion
Wednesday, December 3, 2008 - 1:15pm - 2:15pm
Tong Li (The University of Iowa)
We establish the existence and the stability of traveling wave solutions of quasi-linear hyperbolic systems with both relaxation and diffusion. The traveling wave solutions are shown to be asymptotically stable against small perturbations provided that the diffusion coefficient is bounded by a constant multiple of the relaxation time. The result provides an important first step toward the understanding of the transition from stability to instability as the diffusion coefficient increases.