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.
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A. Raczyński (2009) studied this question.