Degenerate diffusion with a drift potential: a viscosity solutions approach

Details Degenerate diffusion with a drift potential: a viscosity solutions approach Degenerate diffusion with a drift potential: a viscosity solutions approach

2009-10-19

arxiv.org/abs/0910.3432v2

Mathematics

Analysis of PDEs

25 pages, 3 figures

Scientific paper

We introduce a notion of viscosity solutions for a nonlinear degenerate diffusion equation with a drift potential. We show that our notion of solutions coincide with the weak solutions defined via integration by parts. As an application of the viscosity solutions theory, we show that the free boundary uniformly converges to the equilibrium as time grows. In the case of a convex potential, an exponential rate of free boundary convergence is obtained.

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