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arXiv · 2105.03981

Anisotropic p-Laplacian Evolution of Fast Diffusion type

Filomena Feo·Juan Luis Vazquez·Bruno Volzone
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Abstract

We study an anisotropic, possibly non-homogeneous version of the evolution $p$-Laplacian equation when fast diffusion holds in all directions. We develop the basic theory and prove symmetrization results from which we derive $L^1$ to $L^\infty$ estimates. We prove the existence of a self-similar fundamental solution of this equation in the appropriate exponent range, and uniqueness in a smaller range. We also obtain the asymptotic behaviour of finite mass solutions in terms of the self-similar solution. Positivity, decay rates as well as other properties of the solutions are derived. The combination of self-similarity and anisotropy is not common in the related literature. It is however essential in our analysis and creates mathematical difficulties that are solved for fast diffusions.

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Filomena Feo, Juan Luis Vazquez, Bruno Volzone. 2021-05-09. Anisotropic p-Laplacian Evolution of Fast Diffusion type. https://arxiv.org/abs/2105.03981

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