2024-03-29T14:44:35Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698362022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116ON GENERAL EXISTENCE RESULTS FOR ONE-DIMENSIONAL SINGULAR DIFFUSION EQUATIONS WITH SPATIALLY INHOMOGENEOUS DRIVING FORCEGiga, Mi-HoGIGA, YOSHIKAZUNakayasu, Atsushiopen access410A 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.Department of Mathematics, Hokkaido University2013-04-19engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84176http://hdl.handle.net/2115/6983610.14943/84176Hokkaido University Preprint Series in Mathematics1032120https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69836/1/pre1032.pdfapplication/pdf158.53 KB2013-04-19