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A Note on a Model System with Sudden Directional Diffusion

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Abstract

We study qualitative properties of solutions to a monodimensional problem

$$u_t-(u_x + \operatorname{sgn} u_x)_x=0$$

with the Dirichlet boundary conditions. Such a system presents a key analytical challenge coming from the examination of models of anisotropic phenomena like crystal growth. Our analysis concentrates on the properties of facets—flat regions of solutions—typical for this type of problems.

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Acknowledgements

This work has been partly supported by MNiSzW grant No. N N201 268935. Both authors want to thank the referees for their remarks which helped make the paper better.

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  1. Instytut Matematyki Stosowanej i Mechaniki, Uniwersytet Warszawski, ul. Banacha 2, 02-097, Warsaw, Poland

    Piotr Bogusław Mucha & Piotr Rybka

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  1. Piotr Bogusław Mucha
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  2. Piotr Rybka
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Correspondence to Piotr Rybka.

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Mucha, P.B., Rybka, P. A Note on a Model System with Sudden Directional Diffusion. J Stat Phys 146, 975–988 (2012). https://doi.org/10.1007/s10955-012-0446-5

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  • DOI: https://doi.org/10.1007/s10955-012-0446-5

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