光华讲坛——教授论坛2014年第4期



主 题：Global existence and transition-layer steady states of a competition system with advection

主讲人：王琪 副教授

主持人：经济数学学院 张清邦教授

时 间：2014年4月2日（星期三）下午4:00

地 点：柳林校区通博楼B412

主办单位：经济数学学院 科研处
内容提要：

In this talk, we consider a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions, which models a competition relationship that one species escape from the region of high population density of the competitors in order to avoid competitions. The global existence of bounded classical solutions are established for a parabolic-parabolic system over one-dimensional domains and for its parabolic-elliptic counterpart over multi-dimensional domains. We then study the existence and stability of non-constant positive steady states through bifurcation theories. In the limit of large advection rate, we show that this reaction-advection-diffusion system converges to a shadow system and then we study the existence and stability of positive solutions of the shadow system through bifurcation theories. Finally, we construct its positive solutions with an interior transition layer at any predetermined point over the given interval. This talk is based on the recent work joint with Chunyi Gai and Jingda Yan at SWUFE.