Advanced Studies in Pure Mathematics

Models of a sudden directional diffusion

Piotr Bogusław Mucha and Piotr Rybka

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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.

Article information

Variational Methods for Evolving Objects, L. Ambrosio, Y. Giga, P. Rybka and Y. Tonegawa, eds. (Tokyo: Mathematical Society of Japan, 2015), 225-244

Received: 13 March 2013
Revised: 4 September 2013
First available in Project Euclid: 19 October 2018

Permanent link to this document euclid.aspm/1539916038

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B65: Smoothness and regularity of solutions 35K67: Singular parabolic equations

Anisotropy parabolic systems sudden directional diffusion facets


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.

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