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9 papers · 2 filters
Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion
Adrien Blanchet, Philippe Laurencot
For a specific choice of the diffusion, the parabolic-elliptic Patlak-Keller-Segel system with non-linear diffusion (also referred to as the quasi-linear Smoluchowski-Poisson equat…
Nonlocal minimal surfaces
L. A. Caffarelli, J. -M. Roquejoffre, O. Savin
The de Giorgi theory for minimal surfaces consists in studying sets whose indicator function is a (local) minimum of the BV norm. In this paper we replace the BV norm by the …
A new variational approach to the stability of gravitational systems
Mohammed Lemou, Florian Mehats, Pierre Raphael
We consider the three dimensional gravitational Vlasov Poisson system which describes the mechanical state of a stellar system subject to its own gravity. A well-known conjecture i…
Blowup of solutions to a diffusive aggregation model
Piotr Biler, Grzegorz Karch, Philippe Laurençot
The nonexistence of global in time solutions is studied for a class of aggregation equations involving Lévy diffusion operators and general interaction kernels.
Looking for critical nonlinearity in the one-dimensional quasilinear Smoluchowski-Poisson system
Tomasz Cieślak, Philippe Laurençot
It is known that classical solutions to the one-dimensional quasilinear Smoluchowski-Poisson system with nonlinear diffusion may blow up in finite time if a…
Stable ground states for the relativistic gravitational Vlasov-Poisson system
Mohammed Lemou, Florian Mehats, Pierre Raphael
We consider the three dimensional gravitational Vlasov-Poisson (GVP) system in both classical and relativistic cases. The classical problem is subcritical in the natural energy spa…