Abstract
The paper contains results concerning the stability properties of solutions to a simplified Keller–Segel problem modelling chemotaxis in the whole space R2. 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.