DMS Applied Mathematics Seminar

Speaker: Ms. Shuwen Xue (Auburn University)

Title: Dynamics of chemotaxis models with logistic source

Abstract: Chemotaxis models are used to describe the evolution of mobile species subject to chemical substances. In this talk, I will introduce the chemotaxis models with logistic source first. Then, I will talk about parabolic-elliptic chemotaxis model with logistic source. The effects of chemotaxis on spreading speeds and traveling waves will be investigated. Biologically, spreading speeds can be understood as the asymptotic rate at which a species, initially introduced in a bounded range, expands its spatial range as time evolves, while traveling waves describe the propagation of  species as a wave with a fixed shape and a fixed speed. Next, parabolic-elliptic chemotaxis model under climate change will be discussed. The persistence criterion for species and the existence of forced waves will be presented. Forced waves illustrate how the species under consideration would die out at every point. Some numerical simulations will be presented to demonstrate the existence of forced waves.

Join from PC, Mac, Linux, iOS or Android: https://auburn.zoom.us/j/88918338743