[Explosion en temps fini des solutions à symétrie radiale d'un système de Smoluchowski–Poisson quasilinéaire critique]
L'explosion en temps fini est établie pour des solutions à symétrie radiale d'un système de Smoluchowski–Poisson quasilinéaire critique dès que la masse de la donnée initiale dépasse un certain seuil. Dans le cas surcritique, l'explosion peut se produire pour toute masse positive. L'argument principal de la démonstration est une nouvelle identité de type viriel.
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.
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@article{CRMATH_2009__347_5-6_237_0,
author = {Cie\'slak, Tomasz and Lauren\c{c}ot, Philippe},
title = {Finite time blow-up for radially symmetric solutions to a critical quasilinear {Smoluchowski{\textendash}Poisson} system},
journal = {Comptes Rendus. Math\'ematique},
pages = {237--242},
publisher = {Elsevier},
volume = {347},
number = {5-6},
year = {2009},
doi = {10.1016/j.crma.2009.01.016},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.01.016/}
}
TY - JOUR AU - Cieślak, Tomasz AU - Laurençot, Philippe TI - Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski–Poisson system JO - Comptes Rendus. Mathématique PY - 2009 SP - 237 EP - 242 VL - 347 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.01.016/ DO - 10.1016/j.crma.2009.01.016 LA - en ID - CRMATH_2009__347_5-6_237_0 ER -
%0 Journal Article %A Cieślak, Tomasz %A Laurençot, Philippe %T Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski–Poisson system %J Comptes Rendus. Mathématique %D 2009 %P 237-242 %V 347 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.01.016/ %R 10.1016/j.crma.2009.01.016 %G en %F CRMATH_2009__347_5-6_237_0
Cieślak, Tomasz; Laurençot, Philippe. Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski–Poisson system. Comptes Rendus. Mathématique, Tome 347 (2009) no. 5-6, pp. 237-242. doi : 10.1016/j.crma.2009.01.016. http://www.numdam.org/articles/10.1016/j.crma.2009.01.016/
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