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

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 i...

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Veröffentlicht in:	Boundary value problems 2015-08, Vol.2015 (1), p.1-14, Article 127
1. Verfasser:	Piskin, Erhan
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Approximations and Expansions Boundary value problems Damping Decomposition Difference and Functional Equations Energy use Estimates Inequalities Life span Mathematical analysis Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations
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Zusammenfassung:	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.
ISSN:	1687-2770 1687-2762 1687-2770
DOI:	10.1186/s13661-015-0395-4