演讲题目：Minimal wave speed for a class of non-cooperative diffusion-reaction system

演讲人：Tianran Zhang ，School of Mathematics and Statistics, Southwest University, Chongqing

报告摘要（Abstract）: In this paper, we consider a class of non-cooperative diffusion-reaction system, which includes prey-predator and disease-transmission models. The concept of weak traveling wave solutions is defined and the necessary and sufficient conditions are obtained for the existence of weak traveling wave solutions. Finally, these results are applied to prey-predator and disease-transmission models with specific interaction functions. Schauder`s fixed-point theorem and persistence theory are used to show the existence of weak traveling wave solutions, where the introduction of persistence theory is very technical and crucial. LaSalle`s invariance principle is applied to show that traveling wave solutions should connect two equilibria. Nonexistence of traveling wave solutions is proved by introducing the concept of negative one-sided Laplace transform. In this paper, we find that the profile of traveling wave solutions may depend on different eigenvalues according to the corresponding condition, which is a new phenomenon.