Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Variational Methods for Evolving Objects, L. Ambrosio, Y. Giga, P. Rybka and Y. Tonegawa, eds. (Tokyo: Mathematical Society of Japan, 2015), 225 - 244
Models of a sudden directional diffusion
We study degenerate and singular parabolic equations in one space dimension. The emphasis is put on the regularity of solutions and the creation as well as the evolution of facets. Facets are understood as flat parts of the graph of solutions being a result of extremely high singularity. The systems, which we consider, arise from the theory of crystals.
Received: 13 March 2013
Revised: 4 September 2013
First available in Project Euclid: 19 October 2018
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Mucha, Piotr Bogusław; Rybka, Piotr. Models of a sudden directional diffusion. Variational Methods for Evolving Objects, 225--244, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06710225. https://projecteuclid.org/euclid.aspm/1539916038