On the decay and blow up of solutions for a quasilinear hyperbolic equations with nonlinear damping and source terms

被引：14

作者：

Piskin, Erhan ^{[1
]}

机构：

[1] Dicle Univ, Dept Math, Diyarbakir, Turkey

来源：

BOUNDARY VALUE PROBLEMS | 2015年

关键词：

decay; blow up; quasilinear hyperbolic equation; nonlinear damping and source terms; GLOBAL-SOLUTIONS; WAVE-EQUATIONS; EVOLUTION-EQUATIONS; UNIFORM DECAY; EXISTENCE; NONEXISTENCE;

D O I：

10.1186/s13661-015-0395-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we investigate the global existence, decay, and blow up of solutions for a quasilinear hyperbolic equation. We prove the decay estimates of the energy function by using Nakao's inequality. Also, we obtain the blow up of solutions and lifespan estimates in three different ranges of the initial energy.

引用

页数：14

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