Blow-up of solutions for a viscoelastic wave equation with variable exponents

被引：32
|
作者：
Park, Sun-Hye [1 ]
Kang, Jum-Ran [2 ]
机构：
[1] Pusan Natl Univ, Ctr Educ Accreditat, Busan, South Korea
[2] Dong A Univ, Dept Math, Busan 604714, South Korea
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2019年 / 42卷 / 06期
基金：
新加坡国家研究基金会;
关键词：
blow-up; variable exponents; viscoelasticity; wave equation; INITIAL-ENERGY SOLUTIONS; GLOBAL EXISTENCE; NONEXISTENCE; SPACES;
D O I：
10.1002/mma.5501
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a viscoelastic wave equation with variable exponents: utt-Delta u+integral 0tg(t-s)Delta u(s)ds+a|ut|m(x)-2ut=b|u|p(x)-2u,where the exponents of nonlinearity p(center dot) and m(center dot) are given functions and a,b > 0 are constants. For nonincreasing positive function g, we prove the blow-up result for the solutions with positive initial energy as well as nonpositive initial energy. We extend the previous blow-up results to a viscoelastic wave equation with variable exponents.
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页码：2083 / 2097
页数：15
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