Abstract: Chemotaxis models describe the movement of biological organisms or cells in response to chemical gradients in their environment. These models are essential for understanding processes such as bacterial movement toward nutrients, immune cell movement to infection sites, and tumor cell invasion. In this talk, we will discuss both the well-posedness and the long-term dynamics of chemotaxis models on the whole domain. We show that the presence of chemicals generally does not slow down the spreading of cells and, under certain conditions, does not enhance the spreading as well. A novel connection between the cell density and chemical concentration is established through the use of sup- and inf-convolution techniques. Additionally, our numerical simulations uncover a significant phase transition related to the chemical sensitivity constant.

 

This is joint work with Zulaihat Hassan and Wenxian Shen.

 

 

Host: Le Chen