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

LI Ping, LI Feng-jie

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

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

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College of Science, China University of Petroleum,

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.

Received date: 2023-05-11

Online published: 2024-12-11

Supported by

Supported by Shandong Provincial Natural Science Foundation of China (Grant No. ZR2021MA003).

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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

Cite this article

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

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