具有对数非线性项的伪抛物型 p-Laplacian 型方程的初边值问题

doi:10.13371/j.cnki.chin.q.j.m.2023.04.003

数学季刊 ›› 2023, Vol. 38 ›› Issue (4): 360-369.doi: 10.13371/j.cnki.chin.q.j.m.2023.04.003

具有对数非线性项的伪抛物型 p-Laplacian 型方程的初边值问题

College of Mathematics and Information, South China Agricultural University,
Guangzhou 510642, China

收稿日期:2022-07-29 出版日期:2023-12-30 发布日期:2023-12-15
通讯作者: FANG Shao-mei (1964-), female, native of Guangzhou, Guangdong, professor of South China Agricultural University, engages in partial differential equation. E-mail:dz90@scau.edu.cn
作者简介: PAN Jia-hui (1998-), female, native of Shaoguan, Guangdong, graduate student of South China Agricultural University, engages in partial differential equation; FANG Shao-mei (1964-), female, native of Guangzhou, Guangdong, professor of South China Agricultural University, engages in partial differential equation.
基金资助:
Supported by the National Natural Science Foundation of China (Grant No. 11271141).

Initial Boundary Value Problem for Pseudo-Parabolic p-Laplacian Type Equation with Logarithmic Nonlinearity

College of Mathematics and Information, South China Agricultural University,
Guangzhou 510642, China

Received:2022-07-29 Online:2023-12-30 Published:2023-12-15
Contact: FANG Shao-mei (1964-), female, native of Guangzhou, Guangdong, professor of South China Agricultural University, engages in partial differential equation. E-mail:dz90@scau.edu.cn
About author: PAN Jia-hui (1998-), female, native of Shaoguan, Guangdong, graduate student of South China Agricultural University, engages in partial differential equation; FANG Shao-mei (1964-), female, native of Guangzhou, Guangdong, professor of South China Agricultural University, engages in partial differential equation.
Supported by:
Supported by the National Natural Science Foundation of China (Grant No. 11271141).

摘要/Abstract

摘要： In this paper, we study the initial boundary value problem of pseudo-parabolic
p-Laplacian type equation, which be use to model some important physical and biological
phenomena. By using the potential well method, we obtain the global existence, asymptotic
behavior and blow up results of weak solution with subcritical initial energy. Then we
also extend these results to the critical initial energy.

关键词: Pseudo-parabolic equation, p-Laplacian, Logarithmic nonlinearity

Abstract: In this paper, we study the initial boundary value problem of pseudo-parabolic
p-Laplacian type equation, which be use to model some important physical and biological
phenomena. By using the potential well method, we obtain the global existence, asymptotic
behavior and blow up results of weak solution with subcritical initial energy. Then we
also extend these results to the critical initial energy.

Key words: Pseudo-parabolic equation, p-Laplacian, Logarithmic nonlinearity

中图分类号:

O175.29

潘嘉慧, 房少梅. 具有对数非线性项的伪抛物型 p-Laplacian 型方程的初边值问题[J]. 数学季刊, 2023, 38(4): 360-369.

PAN Jia-hui, FANG Shao-mei. Initial Boundary Value Problem for Pseudo-Parabolic p-Laplacian Type Equation with Logarithmic Nonlinearity[J]. Chinese Quarterly Journal of Mathematics, 2023, 38(4): 360-369.

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具有对数非线性项的伪抛物型 p-Laplacian 型方程的初边值问题

Initial Boundary Value Problem for Pseudo-Parabolic p-Laplacian Type Equation with Logarithmic Nonlinearity

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