Talk

Time Global Existence and Asymptotic Behavior of Solutions to Degenerate Quasi-linear Parabolic Systems for Chemotaxis-Growth Models

  • Yoshie Sugiyama (Tsuda College, Tokyo)
G3 10 (Lecture hall)

Abstract

In this talk, the following degenerate parabolic system modelling chemotaxis is considered. (KS):ut=(umuv),xinRN,t>0,τvt=Δvv+u,xinRN,t>0,u(x,0)=u0(x),τv(x,0)=τv0(x),x\RN, where m>1,τ=0or1, and N1. We discuss the existence of a global weak solution of (KS) under some appropriate conditions on m without any restriction on the size of the initial data.

Specifically, it is discussed that a solution (u,v) of (KS) exists globally in time either (i) 2m for large initial data or (ii)1<m22N for small initial data. In the case of (ii), the decay properties of the solution (u,v) are also presented.