Degenerate diffusion with a drift potential: A viscosity solutionsapproach

Inwon C. Kim; Helen K. Lei

doi:10.3934/dcds.2010.27.767

Article Contents

2010, Volume 27, Issue 2: 767-786. Doi: 10.3934/dcds.2010.27.767

This issue Previous Article A Jang equation approach to the Penrose inequality Next Article Omega-limit sets for spiral maps

Degenerate diffusion with a drift potential: A viscosity solutions approach

Inwon C. Kim^1, and
Helen K. Lei^1,

1.
UCLA Mathematics Department, Box 951555, Los Angeles, CA 90095-1555

Received: October 2009

Revised: February 2010

Published: July 2010

Abstract Related Papers Cited by

Abstract

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 $t$ grows. In the case of a convex potential, an exponential rate of free boundary convergence is obtained.

Keywords:

Mathematics Subject Classification: 35D40, 34K21, 35K65.

Citation:

Article Metrics

HTML views() PDF downloads(98) Cited by(0)

Degenerate diffusion with a drift potential: A viscosity solutions approach

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Degenerate diffusion with a drift potential: A viscosity solutions approach

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content