2020/06/08 by Yoshikazu Giga, Giga, Yoshikazu, Norbert Požár +1
Mathematics · Computer Science · Engineering · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques
paper · pdf · doi:10.48550/arxiv.2006.04375
A general purely crystalline mean curvature flow equation with a nonuniform\ndriving force term is considered. The unique existence of a level set flow is\nestablished when the driving force term is continuous and spatially Lipschitz\nuniformly in time. By introducing a suitable notion of a solution a comparison\nprinciple of continuous solutions is established for equations including the\nlevel set equations. An existence of a solution is obtained by stability and\napproximation by smoother problems. A necessary equi-continuity of approximate\nsolutions is established. It should be noted that the value of crystalline\ncurvature may depend not only on the geometry of evolving surfaces but also on\nthe driving force if it is spatially inhomogeneous.\n