Initial boundary value problem for generalized logarithmic improved Boussinesq equation

被引：12

作者：

Hu, Qingying ^{[1
]}

Zhang, Hongwei ^{[1
]}

机构：

[1] Henan Univ Technol, Dept Math, Zhengzhou 450001, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2017年 / 40卷 / 10期

基金：

中国国家自然科学基金;

关键词：

generalized logarithmic improved Boussinesq equation; initial boundary value problem; existence of global solution; exponential growth; decay; DOUBLE DISPERSION-EQUATION; POWER-TYPE NONLINEARITIES; ASYMPTOTIC-BEHAVIOR; GLOBAL EXISTENCE; EXPONENTIAL DECAY; SOLITARY WAVES; CAUCHY-PROBLEM;

D O I：

10.1002/mma.4255

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the initial boundary value problem for generalized logarithmic improved Boussinesq equation. By using the Galerkin method, logarithmic Sobolev inequality, logarithmic Gronwall inequality, and compactness theorem, we show the existence of global weak solution to the problem. By potential well theory, we show the norm of the solution will grow up as an exponential function as time goes to infinity under some suitable conditions. Furthermore, for the generalized logarithmic improved Boussinesq equation with damped term, we obtain the decay estimate of the energy. Copyright (c) 2016 John Wiley & Sons, Ltd.

引用

页码：3687 / 3697

页数：11

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