Global existence and blow up of solution for semilinear hyperbolic equation with logarithmic nonlinearity

被引：44
作者：
Lian, Wei [1 ]
Ahmed, Md Salik [2 ]
Xu, Runzhang [1 ,3 ]
机构：
[1] Harbin Engn Univ, Coll Automat, Harbin 150001, Heilongjiang, Peoples R China
[2] North South Univ, Dept Math & Phys, Dhaka 1229, Bangladesh
[3] Harbin Engn Univ, Coll Math Sci, Harbin 150001, Heilongjiang, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2019年 / 184卷
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Global existence; Infinite time blow up; Logarithmic nonlinearity; Potential well; NONEXISTENCE THEOREMS; POTENTIAL WELLS; DECAY;
D O I：
10.1016/j.na.2019.02.015
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider the semilinear wave equation with logarithmic nonlinearity. By modifying and using potential well combined with logarithmic Sobolev inequality, we derive the global existence and infinite time blow up of the solution at low energy level E(0) < d. Then these results are extended in parallel to the critical case E(0) = d. Besides, with additional assumptions on initial data, the infinite time blow up result is given with arbitrary positive initial energy E(0) > 0. (C) 2019 Elsevier Ltd. All rights reserved.
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页码：239 / 257
页数：19
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