Speaker: Professor Tong Li (Univ. of Iowa)
Title: Stability of traveling waves in quasi-linear
Time: 2008-09-25 (Thu.)  15:00 - 16:00
Abstract: We establish the existence and the stability of traveling wave solutions of a quasi-linear hyperbolic system with both relaxation and diffusion. The traveling wave solutions are shown to be asymptotically stable under small disturbances and under the sub-characteristic condition using a weighted energy method. The delicate balance between the relaxation and the diffusion that leads to the stability of the traveling waves is identified, namely, the diffusion coefficient is bounded by a constant multiple of the relaxation time. Such a result provides an important first step toward the understanding of the transition from stability to instability as parameters vary in physical problems involving both relaxation and diffusion.
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