Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski-Poisson system

2008/10/19 by Tomasz Cieślak, Cieślak, Tomasz, Philippe Laurençot +1 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.0810.3367

arxiv created 2008/10/19 · arxiv updated 2009/12/01

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.

Citations

• On explosions of solutions to a system of partial differential equations modelling chemotaxis

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• Critical mass for finite-time chemotactic collapse in the critical dimension via comparison

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