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Quenching Phenomenon for A Degenerate Parabolic Equation with a Singular Boundary Flux

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Abstract

A quenching phenomenon of a degenerate parabolic equation with nonlinear source and singular boundary condition in one-dimensional space is investigated. We establish the results that quenching will occur in a finite time on the boundary x = 0 or x = 1, respectively. And the blowing up of ut at the quenching point and quenching rate estimates are discussed.

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Acknowledgments

The author would like to thank the anonymous referee sincerely for the valuable suggestions and comments in improving the paper.

Funding

The author is partially supported by the Guangdong Basic and Applied Basic Research Foundation (No. 2020A1515010446), National Science Foundation of China (No. 11971320, No. 11671155, and No. 11701384), and China Scholarship Council under grants 201908440614.

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  1. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Ying Yang

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  1. Ying Yang
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Correspondence to Ying Yang.

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Yang, Y. Quenching Phenomenon for A Degenerate Parabolic Equation with a Singular Boundary Flux. J Dyn Control Syst 27, 477–489 (2021). https://doi.org/10.1007/s10883-020-09494-2

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  • DOI: https://doi.org/10.1007/s10883-020-09494-2

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