Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion
نویسنده
چکیده
For a specific choice of the diffusion, the parabolic-elliptic PatlakKeller-Segel system with non-linear diffusion (also referred to as the quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold phenomenon: there is a critical mass Mc > 0 such that all the solutions with initial data of mass smaller or equal to Mc exist globally while the solution blows up in finite time for a large class of initial data with mass greater than Mc. Unlike in space dimension 2, finite mass self-similar blowing-up solutions are shown to exist in space dimension d ≥ 3.
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