Blow-up of solutions to a quasilinear wave equation for high initial energy

被引：5
|
作者：
Li, Fang [1 ]
Liu, Fang [2 ]
机构：
[1] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China
[2] Changchun Univ Technol, Sch Basic Sci, Changchun 130012, Jilin, Peoples R China
来源：
COMPTES RENDUS MECANIQUE | 2018年 / 346卷 / 05期
关键词：
Viscoelastic hyperbolic equation; Energy estimate method; High initial energy; HYPERBOLIC-EQUATIONS; EXISTENCE; T)-LAPLACIAN; TIME; P(X;
D O I：
10.1016/j.crme.2018.03.002
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
This paper deals with blow-up solutions to a nonlinear hyperbolic equation with variable exponent of nonlinearities. By constructing a new control function and using energy inequalities, the authors obtain the lower bound estimate of the L-2 norm of the solution. Furthermore, the concavity arguments are used to prove the nonexistence of solutions; at the same time, an estimate of the upper bound of blow-up time is also obtained. This result extends and improves those of [1,2]. (C) 2018 Published by Elsevier Masson SAS on behalf of Academie des sciences.
引用
收藏
页码：402 / 407
页数：6
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