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

Boundary value problems

Erhan Pikin¹ 

[1] Department of Mathematics, Dicle University, Diyarbakir, Turkey

关键词: decay;    blow up;    quasilinear hyperbolic equation;    nonlinear damping and source terms;    35B40;    35B44;    35L72;   

DOI  :  10.1186/s13661-015-0395-4

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY