DMS Graduate Student Seminar

Speaker: Professor Wenxian Shen

Title: Dynamics in chemotaxis models of parabolic-elliptic type on bounded heterogeneous environments

Abstract: In this talk, I will first derive briefly chemotaxis models, point out their importance, interesting dynamical questions related to chemotaxis models and some of the existing works. Next I will present some of our results on dynamics of one-species chemotaxis models of parabolic-elliptic type in heterogeneous environments. First, we will discuss our result on local existence and uniqueness of solutions.

Next, the result on boundedness and global existence of solutions which is proved under some natural parameter regions. Then the result on the existence of a positive entire solution which is proved under the same parameter regions of global existence. Finally, the result on uniqueness and nonlinear stability of positive entire solutions which is proved under some further parameter regions.