Surface evolution equations : a level set approach

By 儀我美一. 2006

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Well-posedness of Hamilton–Jacobi equations with Caputo’s time fractional derivative (2016, background): “The reader is referred to [1, 4, 24] for basic theory and to [7, 13] for more advanced theory.”
On the mean curvature flow of grain boundaries (2015, background): “he velocity is equal to its mean curvature at each point and time. Since the 1970’s, the MCF has been studied by numerous researchers as it is one of the fundamental geometric evolution problems (see [5, 14, 15, 24, 36] for the overview and references related to the MCF) appearing in ﬁelds such as d”
COMPACT EMBEDDED HYPERSURFACES WITH CONSTANT HIGHER ORDER ANISOTROPIC MEAN CURVATURES (2007, background): “Theorem, which gives an affirmative answer to the following open problem proposed by Morgan in the same paper and by Giga in [6]: Must an embedded equilibrium, i.”
Shape and topology optimization based on the phase field method and sensitivity analysis (2010, methodology): “The level set method was originally proposed by Osher and Sethian [20] as a numerical method for tracking free boundaries according to the mean-curvature motion, and the mathematical background was subsequently clarified by several researchers [21, 22, 23].”