Blow-Up and Decay Estimate in a Logarithmic p-Laplace Parabolic Equation

doi:10.13371/j.cnki.chin.q.j.m.2024.04.001

Chinese Quarterly Journal of Mathematics ›› 2024, Vol. 39 ›› Issue (4): 331-354.doi: 10.13371/j.cnki.chin.q.j.m.2024.04.001

College of Science, China University of Petroleum,

Received:2023-05-11 Online:2024-12-30 Published:2024-12-11
Contact: LI Feng-jie (1974-), female, native of Yantai, Shandong, associate professor of China University of Petroleum, engages in partial differential equations. E-mail:fjli@upc.edu.cn
About author:LI Ping (1999-), female, native of Hengshui, Hebei, master student of China University of Petroleum, engages in partial differential equations; LI Feng-jie (1974-), female, native of Yantai, Shandong, associate professor of China University of Petroleum, engages in partial differential equations.
Supported by:
Supported by Shandong Provincial Natural Science Foundation of China (Grant No. ZR2021MA003).

Abstract

Abstract: This paper deals with an initial-boundary value problem of a fourth-order parabolic equation involving Logarithmic type p-Laplacian, which could be proposed as a model for the epitaxial growth of thin films. By using the variational method and the
logarithmic type Sobolev inequality, we give some threshold results for blow-up solutions and global solutions, which could be classified by the initial energy. The asymptotic estimates about blow-up time and decay estimate of weak solutions are obtained.

Key words: High order parabolic equation, Blow-up time, Decay estimate, Global existence, Logarithmic type p-Laplacian

CLC Number:

O175.4

LI Ping, LI Feng-jie. Blow-Up and Decay Estimate in a Logarithmic p-Laplace Parabolic Equation[J]. Chinese Quarterly Journal of Mathematics, 2024, 39(4): 331-354.

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Blow-Up and Decay Estimate in a Logarithmic p-Laplace Parabolic Equation

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