Blowup rate of solutions of a degenerate nonlinear parabolic equation

Chi-Cheung Poon

doi:10.3934/dcdsb.2019060

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2019, Volume 24, Issue 10: 5317-5336. Doi: 10.3934/dcdsb.2019060

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Blowup rate of solutions of a degenerate nonlinear parabolic equation

Chi-Cheung Poon

Department of Mathematics, National Chung Cheng University, Min-Hsiung, Chia-Yi 621, Taiwan

Received: April 30, 2018

Revised: August 31, 2018

Early access: April 2019

Published: August 2019

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Abstract

We study a nonlinear parabolic equation arising from heat combustion and plane curve evolution problems. Suppose that a solution satisfies a symmetry condition and blows up of type Ⅱ. We give an upper bound and a lower bound for the blowup rate of the solution. The lower bound obtained here is probably optimal.

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Mathematics Subject Classification: 35K20, 35K55, 35K65.

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