Slow growth of solutions of super-fast diffusion equations with unbounded initial data

Marek Fila; Michael Winkler

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arXiv · 1605.04150

Slow growth of solutions of super-fast diffusion equations with unbounded initial data

Marek Fila·Michael Winkler

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Abstract

We study positive solutions of the super-fast diffusion equation in the whole space with initial data which are unbounded as $|x|\to\infty$. We find an explicit dependence of the slow temporal growth rate of solutions on the initial spatial growth rate. A new class of self-similar solutions plays a significant role in our analysis.

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Marek Fila, Michael Winkler. 2016-05-13. Slow growth of solutions of super-fast diffusion equations with unbounded initial data. https://arxiv.org/abs/1605.04150

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