SUMMARYThe existence, uniqueness and large time behaviour of radially symmetric solutions to a chemotaxis system in the plane R 2 are studied either for the critical value of the mass equal to 8 or in the subcritical case.

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We study the existence of stationary and evolution solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles.

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Abstract. We study asymptotic behavior of radial solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles. In particular, we consider stationary solutions in balls and in the whole space, self-similar solutions defined globally in time, blowing up self-similar solutions, and singularities of solutions that blow up in a finite time.