PDE Seminar (2018/10/19): Boundedness of solutions to the Cauchy problem for an attraction-repulsion chemotaxis system

Date
2018-10-19 16:30 - 2018-10-19 17:30
Place
Faculty of Science Building #3, Room 309
Speaker/Organizer
Toshitaka Nagai (Hiroshima University)
 
We consider the Cauchy problem for an attraction-repulsion chemotaxis system in two-dimensional space. The system consists of three partial differential equations; a drift-diffusion equation incorporating terms for both chemoattraction and chemorepulsion, and two elliptic equations. It is known that there is a blowing-up solution in finite time to the Cauchy problem in the attractive dominant case where the coefficient of the attractant is larger than that of the repellent.
In this talk, we discuss the boundedness of nonnegative solutions to the Cauchy problem.