Stability Property Of The Two-dimensional Keller-segel Model

摘要

The paper contains results concerning the stability properties of solutions to a simplified Keller-Segel problem modelling chemotaxis in the whole space R~2. First, the existence of solutions to considered system is proved, as well as for this system with the elliptic equation replaced by its parabolic version with time derivative multiplied by a positive parameter ε. Secondly, the stability of the model is shown, namely the convergence of solutions of parabolic-parabolic system to a solution of parabolic-elliptic one, when a suitable parameter in the system under consideration converges towards zero.