Blow-up of solution for a nonlinear Petrovsky type equation with memory

被引：61
|
作者：
Li, Fushan [1 ]
Gao, Qingyong [1 ]
机构：
[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2016年 / 274卷
基金：
中国国家自然科学基金;
关键词：
Nonlinear Petrovsky equation; Memory; Initial energy; Blow-up; GLOBAL NONEXISTENCE; INITIAL-ENERGY; WAVE-EQUATION; EXISTENCE; DISSIPATION;
D O I：
10.1016/j.amc.2015.11.018
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the nonlinear Petrovsky type equation u(u) + Delta(2)u - integral(t)(0) g?(t - s) Delta(2)u(t, s)ds + vertical bar u(t)vertical bar(m-2)u(t) = vertical bar u vertical bar(p-2)u with initial conditions and Dirichlet boundary conditions. Under suitable conditions of the initial data and the relaxation function, we prove that the solution with upper bounded initial energy blows up in finite time. Moreover, for the linear damping case, we show that the solution blows up in finite time by different method for nonpositive initial energy. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：383 / 392
页数：10
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