臺灣大學數學系演講公告 博士生論文口試

Speaker：張覺心

Title：競爭擴散系統的行波解
         Travelling Wave Solutions of Reaction-Diffusion Systems

Abstract：In population ecology, coexistence and exclusion are central problems for competiting species. Travelling wave solution can be partially used to answer the question about the competition behavior between species. In this talk, we consider the travelling waves of two types of competition-diffusion systems. One is 3-species Lotka-Volterra competition-diffusion systems (3LV), the other is a free boundary problem for a two-species competitive model (2FB). For (3LV), a travelling wave solution can be considered as a heteroclinic orbit of a vector field in R^6. Under suitable assumptions on the parameters of the equations, we apply a bifurcation theory of heteroclinic orbits to show that a 3-species travelling wave can bifurcate from two 2-species waves which connect to a common equilibrium. The three components of the 3-species wave obtained are positive and have the profiles that one component connects a positive state to zero, one component connects zero to a positive state, and the third component is a pulse between the previous two with a long middle part close to a positive constant. The model (2FB) was proposed by Mimura, Yamada and Yotsutani in 1985. Motivated by the spreading-vanishing dichotomy results for one species case, we suppose the spreading speed of the free boundary tends to a constant as time tends to infinity and consider the corresponding travelling wave problem. We establish the existence and uniqueness of a travelling wave solution for this free boundary problem.

Time：15:00 - 16:00, June. 04(Mon.), 2012

Place：Room 430, Astronomy and Mathematics Building, National Taiwan University(臺灣大學天文數學館430室)