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- Mi-Ho Giga, Yoshikazu Giga
- 2013

We extend the theory of viscosity solutions to a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of an arbitrary dimension with diffusion given by an anisotropic total variation energy. We give a proof of a comparison principle, an outline of a proof of the stability under approximation by regularized… (More)

- Mi-Ho Giga, Yoshikazu Giga, Norbert Požár
- 2013

We introduce a new notion of viscosity solutions for a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of arbitrary dimension, whose diffusion on flat parts with zero slope is so strong that it becomes a nonlocal quantity. The problems include the classical total variation flow and a motion of a surface by a… (More)

- Hidekata Hontani, Mi-Ho Giga, Yoshikazu Giga, Koichiro Deguchi
- Discrete Applied Mathematics
- 2005

A n umerical method for obtaining a crystalline ow starting from a general polygon is presented. A crystalline ow is a polygonal ow and can be regarded as a discrete version of a classical curvature ow. In some cases, new facets may be created instantaneously and their facet lengths are governed by a system of singular ordinary dierential equations (ODEs).… (More)

- Mi-Ho Giga, Yoshikazu Giga, Hidekata Hontani
- SIAM J. Math. Analysis
- 2005

- Hidekata Hontani, Mi-Ho Giga, Yoshikazu Giga, Koichiro Deguchi
- DGCI
- 2003

- Hidekata Hontani, Yu Suzuki, Yoshikazu Giga, Mi-Ho Giga, Koichiro Deguchi
- Scale-Space
- 2005

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