Global existence vs. blowup for the one dimensional quasilinear Smoluchowski-Poisson system

Tomasz Cieslak (1) , Philippe Laurencot (2)

1 IMSM - Institute of Applied Mathematics [Warsaw]
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We prove that, unlike in several space dimensions, there is no critical (nonlinear) diffusion coefficient for which solutions to the one dimensional quasilinear Smoluchowski-Poisson equation with small mass exist globally while finite time blowup could occur for solutions with large mass.

Mots clés: nonlinear diffusion; blowup; global existence

Domaines: Equations aux dérivées partielles [math.AP]

Tomasz Cieslak, Philippe Laurencot. Global existence vs. blowup for the one dimensional quasilinear Smoluchowski-Poisson system. Escher, J.; Guidotti, P.; Hieber, M.; Mucha, P.; Prüss, J.W.; Shibata, Y.; Simonett, G.; Walker, C.; Zajaczkowski, W. Parabolic Problems. The Herbert Amann Festchrift, Springer, pp.95--109, 2011, Progr. Nonlinear Differential Equations Appl., 978-3-0348-0074-7. ⟨hal-00453540⟩