GLOBAL EXISTENCE AND ENERGY DECAY ESTIMATE OF SOLUTIONS FOR A CLASS OF NONLINEAR HIGHER-ORDER WAVE EQUATION WITH GENERAL NONLINEAR DISSIPATION AND SOURCE TERM

被引：0
|
作者：
Zhou, Jun [1 ]
机构：
[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2017年 / 10卷 / 05期
基金：
中国博士后科学基金;
关键词：
Higher-order wave equation; general nonlinear dissipation; global existence; decay; BLOW-UP; NONEXISTENCE; PETROVSKY; SYSTEM;
D O I：
10.3934/dcdss.2017064
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with a higher-order wave equation with general nonlinear dissipation and source term u '' + (Delta)(m) u + g(u') = b vertical bar u vertical bar(p-2) u, which was studied extensively when m = 1, 2 and the nonlinear dissipative term g(u') is a polynomial, i.e., g(u') - a vertical bar u'vertical bar(q-2)u'. We obtain the global existence of solutions and show the energy decay estimate when m >= 1 is a positive integer and the nonlinear dissipative term g does not necessarily have a polynomial grow near the origin.
引用
收藏
页码：1175 / 1185
页数：11
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