ON GENERAL EXISTENCE RESULTS FOR ONE-DIMENSIONAL SINGULAR DIFFUSION EQUATIONS WITH SPATIALLY INHOMOGENEOUS DRIVING FORCE

A general anisotropic curvature flow equation with singular in- terfacial energy and spatially inhomogeneous driving force is considered for a curve given by the graph of a periodic function. We prove that the initial value problem admits a unique global-in-time viscosity solution for a general periodic continuous initial datum. The notion of a viscosity solution used here is the same as proposed by Giga, Giga and Rybka, who established a compar- ison principle. We construct the global-in-time solution by careful adaptation of Perron's method