Colloquium / Seminars

Topic：2016 NCTS/CMMSC Seminar on Dynamical Systems and PDEs
Speaker：Dr. Chueh-Hsin Chang
　　　　(Taida Institute for Mathematical Sciences, National Taiwan University)
Date time：Jan. 15 2016, 15:00~16:30
Venue：NCTU SA307
Abstract：
Title：(1) Stability of the trivial three-species waves
in the Lotka-Volterra competition-diffusion systems
(2) Long-time asymptotics of Camassa-Holm equations

Abstract：
In this talk, two topics will be discussed. In the first part, we consider the stability of the trivial three-species traveling waves in the Lotka-Volterra competition-diffusion systems. The motivation of this work coming from the problems about competition-mediated coexistence. That is, suppose there are two species under strong competition in an environment. If a third species invades the system, the original competing two species maybe changed from non-coexistence to be coexistence. In the second part of this talk, we consider Camassa-Holm (CH) equations. This is one of the shallow water wave equations with the special features different from KdV equations that the peakon phenomenon can be observed. Among the analysis of solutions, the long-time asymptotics is one of the important topics since the corresponding tools about integrable systems needed to be considered. We use the inverse scattering transform which is a generalization of the Fourier transform to construct a specified initial condition of CH equations. Under this initial condition, the dynamics of solutions are analyzed numerically. Then the previous obtained long-time results can be verified in a more visible way.

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