2013 | OriginalPaper | Buchkapitel
On general existence results for one-dimensional singular diffusion equations with spatially inhomogeneous driving force
Erschienen in: Geometric Partial Differential Equations proceedings
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A general anisotropic curvature flow equation with singular interfacial 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 comparison principle. We construct the global-in-time solution by careful adaptation of Perron’s method.