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  

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

作　　者：江东月 唐忠华 房少梅 JIANG Dong-yue;TANG Zhong-hua;FANG Shao-mei(College of Mathematics and Informatics,South China Agricultural University,Guangzhou 510642,China)

机构地区：[1]College of Mathematics and Informatics,South China Agricultural University,Guangzhou 510642,China

出　　处：《Chinese Quarterly Journal of Mathematics》2024年第2期111-127,共17页数学季刊（英文版）

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

摘　　要：In this paper,a semilinear pseudo-parabolic equation with a general nonlin-earity 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 Blow-up time 

分 类 号：O187.1[理学—数学]