数学季刊 ›› 2024, Vol. 39 ›› Issue (4): 331-354.doi: 10.13371/j.cnki.chin.q.j.m.2024.04.001

• •    下一篇

一类对数p-Laplace抛物型方程中的爆破和衰减估计

  

  1. College of Science, China University of Petroleum,
  • 收稿日期:2023-05-11 出版日期:2024-12-30 发布日期:2024-12-11
  • 通讯作者: 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
  • 作者简介: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.
  • 基金资助:
    Supported by Shandong Provincial Natural Science Foundation of China (Grant No. ZR2021MA003).

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

  1. 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).

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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

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

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