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Global Existence, Extinction, and Non-Extinction of Solutions to a Fast Diffusion p-Laplace Evolution Equation with Singular Potential

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Abstract

In this paper, we study a class of fast diffusion p-Laplace equation with singular potential in a bounded smooth domain with homogeneous Dirichlet boundary condition. By using energy estimates, Hardy-Littlewood-Sobolev inequality, and some ordinary differential inequalities, we get the solution of the equation exists globally. Moreover, the conditions of extinction and non-extinction are studied. The results of this paper extend and complete the previous studies on this equation.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, People’s Republic of China

    Xiumei Deng & Jun Zhou

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  1. Xiumei Deng
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  2. Jun Zhou
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Correspondence to Jun Zhou.

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This work is supported by NSFC (Grant No. 11201380).

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Deng, X., Zhou, J. Global Existence, Extinction, and Non-Extinction of Solutions to a Fast Diffusion p-Laplace Evolution Equation with Singular Potential. J Dyn Control Syst 26, 509–523 (2020). https://doi.org/10.1007/s10883-019-09462-5

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  • DOI: https://doi.org/10.1007/s10883-019-09462-5

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