Nonlocal spatially inhomogeneous Hamilton-Jacobi equation  with unusual free boundary

Yoshikazu Giga; Przemysław Górka; Piotr Rybka

doi:10.3934/dcds.2010.26.493

Article Contents

2010, Volume 26, Issue 2: 493-519. Doi: 10.3934/dcds.2010.26.493

This issue Previous Article On some strong ratio limit theorems for heat kernels Next Article The validity of the Euler-Lagrange equation

Nonlocal spatially inhomogeneous Hamilton-Jacobi equation with unusual free boundary

1.
Graduate School of Mathematical Sciences, University of Tokyo, Komaba 3-8-1, Tokyo 153-8914
2.
Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca
3.
Institute of Applied Mathematics and Mechanics, Warsaw University, ul. Banacha 2, 07-097 Warsaw

Received: December 31, 2008

Revised: June 30, 2009

Published: June 2010

Abstract Related Papers Cited by

Abstract

We consider the weighted mean curvature flow in the plane with a driving term. For certain anisotropy functions this evolution problem degenerates to a first order Hamilton-Jacobi equation with a free boundary. The resulting problem may be written as a Hamilton-Jacobi equation with a spatially non-local and discontinuous Hamiltonian. We prove existence and uniqueness of solutions. On the way we show a comparison principle and a stability theorem for viscosity solutions.

Keywords:

Mathematics Subject Classification: Primary: 49L25; Secondary: 53C44.

Citation:

Article Metrics

HTML views() PDF downloads(110) Cited by(0)

Nonlocal spatially inhomogeneous Hamilton-Jacobi equation with unusual free boundary

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Nonlocal spatially inhomogeneous Hamilton-Jacobi equation with unusual free boundary

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content