Abstract
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.
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Giga, MH., Giga, Y., Nakayasu, A. (2013). On general existence results for one-dimensional singular diffusion equations with spatially inhomogeneous driving force. In: Chambolle, A., Novaga, M., Valdinoci, E. (eds) Geometric Partial Differential Equations proceedings. CRM Series, vol 15. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-473-1_8
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DOI: https://doi.org/10.1007/978-88-7642-473-1_8
Publisher Name: Edizioni della Normale, Pisa
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