Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski–Poisson system |
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| Authors: | Tomasz Cieślak Philippe Laurençot |
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| Institution: | 1. Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland;2. Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université de Toulouse, 118, route de Narbonne, 31062 Toulouse cedex 9, France |
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| Abstract: | Finite time blow-up is shown to occur for radially symmetric solutions to a critical quasilinear Smoluchowski–Poisson system provided that the mass of the initial condition exceeds an explicit threshold. In the supercritical case, blow-up is shown to take place for any positive mass. The proof relies on a novel identity of virial type. To cite this article: T. Cie?lak, P. Laurençot, C. R. Acad. Sci. Paris, Ser. I 347 (2009). |
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