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arXiv · 1402.6877

Transformations of Self-Similar Solutions for porous medium equations of fractional type

Diana Stan·Félix del Teso·Juan Luis Vázquez
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Abstract

We consider four different models of nonlinear diffusion equations involving fractional Laplacians and study the existence and properties of classes of self-similar solutions. Such solutions are an important tool in developing the general theory. We introduce a number of transformations that allow us to map complete classes of solutions of one equation into those of another one, thus providing us with a number of new solutions, as well as interesting connections. Special attention is paid to the property of finite propagation.

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Diana Stan, Félix del Teso, Juan Luis Vázquez. 2014-02-27. Transformations of Self-Similar Solutions for porous medium equations of fractional type. https://arxiv.org/abs/1402.6877

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