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Slow growth of solutions of superfast diffusion equations with unbounded initial data

We study positive solutions of the superfast diffusion equation in the whole space with initial data which are unbounded as |x|→∞. 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 significan...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 2017-04, Vol.95 (2), p.659-683
Main Authors: Fila, Marek, Winkler, Michael
Format: Article
Language:English
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Summary:We study positive solutions of the superfast diffusion equation in the whole space with initial data which are unbounded as |x|→∞. 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.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms.12029