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arXiv · 1207.4929

Well-posedness of sudden directional diffusion equations

Piotr Bogusław Mucha·Piotr Rybka
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Abstract

Our goal is to establish existence with suitable initial data of solutions to general parabolic equation in one dimension, $u_t = L(u_x)_x$, where $L$ is merely a monotone function. We also expose the basic properties of solutions, concentrating on maximal possible regularity. Analysis of solutions with convex initial data explains why we may call them {\it almost classical}. Some qualitative aspects of solutions, like facets -- flat regions of solutions, are studied too.

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Piotr Bogusław Mucha, Piotr Rybka. 2012-07-20. Well-posedness of sudden directional diffusion equations. https://arxiv.org/abs/1207.4929

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