Applied Mathematics Seminar

Speaker: Rachidi  Salako 

Title:  Global existence and asymptotic behavior of classical solutions to a parabolic-elliptic chemotaxis system with logistic source on \(R^N\) 

Abstract: Keller-Segel equations are used to illustrate the time evolution of mobile species toward the gradient of a chemical substance. Such systems are referred  to as chemotaxis systems. Considering the classical Keller-Segel Parabolic-Elliptic/Parabolic chemotaxis systems, in the absence of logistic source, it is known that finite-time blow up of nonnegative solutions can occur when the spatial dimension is greater or equal to 2, but never occurs in the case that the spatial dimension is equal to 1.  In this talk, we consider a Parabolic-Elliptic chemotaxis system with logistic source and prove (i) Local /Global existence of classical solution for various nonnegative initial functions, (ii) Asymptotic behavior of classical solutions. We shall also discuss about some ongoing works about the existence of front propagation and spreading speeds.