一类对数p-Laplace抛物型方程中的爆破和衰减估计

李 平, 李锋杰

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

数学季刊 >

2024 , Vol. 39 >Issue 4: 331 - 354

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

一类对数p-Laplace抛物型方程中的爆破和衰减估计

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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.

收稿日期: 2023-05-11

网络出版日期: 2024-12-11

基金资助

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

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

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College of Science, China University of Petroleum,

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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摘要

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.

关键词： High order parabolic equation; Blow-up time; Decay estimate; Global existence; Logarithmic type p-Laplacian

本文引用格式

李平, 李锋杰 . 一类对数p-Laplace抛物型方程中的爆破和衰减估计[J]. 数学季刊, 2024 , 39(4) : 331 -354 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.001

Abstract

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

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