Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory
| dc.creator | Agueh, Martial | |
| dc.date | 2003-09-24 | |
| dc.date.accessioned | 2026-07-07T05:01:25Z | |
| dc.date.available | 2026-07-07T05:01:25Z | |
| dc.description | We obtain solutions of the nonlinear degenerate parabolic equation \[ \frac{\partial ρ}{\partial t} = {div} \Big\{ρ\nabla c^\star [ \nabla (F^\prime(ρ)+V) ] \Big\} \] as a steepest descent of an energy with respect to a convex cost functional. The method used here is variational. It requires less uniform convexity assumption than that imposed by Alt and Luckhaus in their pioneering work \cite{luckhaus:quasilinear}. In fact, their assumption may fail in our equation. This class of problems includes the Fokker-Planck equation, the porous-medium equation, the fast diffusion equation, and the parabolic p-Laplacian equation. | |
| dc.description | LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0309410 | |
| dc.identifier | http://arxiv.org/abs/math/0309410 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68667 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory | |
| dc.type | text |