数学季刊 ›› 2024, Vol. 39 ›› Issue (2): 111-127.doi: 10.13371/j.cnki.chin.q.j.m.2024.02.001

• •    下一篇

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

江东月, 唐忠华, 房少梅   

  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China
  • 收稿日期:2023-08-30 出版日期:2024-06-30 发布日期:2024-06-30
  • 通讯作者: FANG Shao-mei (1964-), female, native of Huaibei, Anhui, professor of South China Agricultural University, engages in partial differential equation. E-mail: dz90@scau.edu.cn
  • 作者简介: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.
  • 基金资助:
     Supported by National Natural Science Foundation of China (Grant No. 11271141).

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

JIANG Dong-yue, TANG Zhong-hua, FANG Shao-mei   

  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China
  • Received:2023-08-30 Online:2024-06-30 Published:2024-06-30
  • Contact: FANG Shao-mei (1964-), female, native of Huaibei, Anhui, professor of South China Agricultural University, engages in partial differential equation. E-mail: dz90@scau.edu.cn
  • About author: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.
  • 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

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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