NONLOCAL SPATIALLY INHOMOGENEOUS HAMILTON-JACOBI EQUATION WITH UNUSUAL FREE BOUNDARY

作者：Giga Yoshikazu^*; Gorka Przemyslaw; Rybka Piotr

来源：Discrete and Continuous Dynamical Systems, 2010, 26(2): 493-519.

DOI：10.3934/dcds.2010.26.493

• driven curvature flow
• singular energies
• Hamilton-Jacobi equation
• free boundary
• discontinuous Hamiltonian
• comparison principle

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.

• 出版日期2010-2