Global Existence and Blow-Up for a Chemotaxis System

Abstract

Abstract. In this paper we consider a Keller-Segel-type chemotaxis model with reaction term under no-flux boundary conditions, where the kinetics term of the system is power function. Assuming some growth conditions, the existence of bounded global strong solution to the parabolic-parabolic system is given. We also give the numerical test and find out that there exists a threshold. When the power frequency greater than the threshold, both global solution and blow-up solution exist.

Comparison of two finite element schemes for a chemo-repulsion system with quadratic production

“…Then, taking ū = û in (7) and testing ( 8) by v = − 1 2 v, one arrives at (see [12] for more details)…”

“…One of the most important characteristics of chemoattractant models is that the blow-up of solutions can happen in space dimension greater or equal to 2; while in chemo-repulsion models this phenomenon is not expected. Many works have been devoted to study in what cases and how blow-up takes place (see for instance [4,20,25,24,27,7,30]).…”