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

被引：35

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.

引用

页码：2083 / 2097

页数：15

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