Applied Math Seminar
Thursday, September 26th
11:00 AM
Zoom: https://wpi.zoom.us/j/3308040066 and Stratton Hall 201
Speaker: Hewan Shemtaga (Auburn University)
Host: Yonatan Ashenafi (WPI)
Title: Global existence and asymptotic behavior of chemotaxis models on a compact metric graph
Abstract: Chemotaxis is the directed movement of microorganisms in response to chemical stimuli. We investigate a pair of logistic type Keller–Segel systems of reaction-advection-diffusion equations modeling chemotaxis on networks. The distinction between the two systems is driven by the rate of diffusion of chemo-attractant. We prove the global existence of classical solution subject to Neumann-Kirchhoff vertex conditions without any conditions on chemotaxis sensitivity. In addition, we show that solutions with a non-negative and non-zero initial function converge to a globally stable constant solution for relatively small chemotaxis sensitivity. However, as chemotaxis sensitivity increase, we prove the constant solution loses stability and there exist other non-constant steady states bifurcating from the constant solution. This is a joint work with Dr. Wenxian Shen (Auburn) and Dr. Selim Sukhtaiev (Auburn).