数学季刊 >

2024 , Vol. 39 >Issue 2: 111 - 127

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.02.001

具有奇异势和一般非线性的伪抛物方程解的局部存在性和爆破

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  • College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China
FANG Shao-mei (1964-), female, native of Huaibei, Anhui, professor of South China Agricultural University, engages in partial differential equation; JIANG Dong-yue (1998-), male, native of Shaoguan, Guangdong, graduate student of South China Agricultural University, engages in partial differential equation; TANG Zhong-hua (1996-), male, native of Chongqing, Guangdong, graduate student of South China Agricultural University, engages in partial differential equation.

收稿日期: 2023-08-30

  网络出版日期: 2024-06-30

基金资助

 Supported by National Natural Science Foundation of China (Grant No. 11271141).

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Local Existence and Blow-Up of Solutions for Pseudo-Parabolic Equation with Singular Potential and General Nonlinearity

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  • College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China
FANG Shao-mei (1964-), female, native of Huaibei, Anhui, professor of South China Agricultural University, engages in partial differential equation; JIANG Dong-yue (1998-), male, native of Shaoguan, Guangdong, graduate student of South China Agricultural University, engages in partial differential equation; TANG Zhong-hua (1996-), male, native of Chongqing, Guangdong, graduate student of South China Agricultural University, engages in partial differential equation.

Received date: 2023-08-30

  Online published: 2024-06-30

Supported by

 Supported by National Natural Science Foundation of China (Grant No. 11271141).

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摘要

In this paper, a semilinear pseudo-parabolic equation with a general nonlinearity and singular potential is considered. We prove the local existence of solution by Galerkin method and contraction mapping theorem. Moreover, we prove the blow-up of solution and estimate the upper bound of the blow-up time for J(u0)≤0. Finally, we prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0.

关键词： Pseudo-parabolic equation; Singular potential; General nonlinearity; Local existence; Blowup time

本文引用格式

江东月, 唐忠华, 房少梅 . 具有奇异势和一般非线性的伪抛物方程解的局部存在性和爆破[J]. 数学季刊, 2024 , 39(2) : 111 -127 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.001

Abstract

In this paper, a semilinear pseudo-parabolic equation with a general nonlinearity and singular potential is considered. We prove the local existence of solution by Galerkin method and contraction mapping theorem. Moreover, we prove the blow-up of solution and estimate the upper bound of the blow-up time for J(u0)≤0. Finally, we prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0.

Key words： Pseudo-parabolic equation; Singular potential; General nonlinearity; Local existence; Blowup time

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