Lower Bounds for the Blow up Time to a Coupled Nonlinear Hyperbolic Type Equations

Year 2020, Volume: 3 Issue: 1, 53 - 56, 25.03.2020

Erhan Pişkin , Yavuz Dinç , Prof.dr.cemil Tunc

https://doi.org/10.33434/cams.679721

Cited By: 1

Abstract

The initial and Dirichlet boundary value problem of nonlinear hyperbolic type equations in a bounded domain is studied. We established a lower bounds for the blow up time.

Keywords

Lower bounds, Hyperbolic type equations, Nonlinear damping term

References

• [1] J. Wu, S. Li, S. Chai, Existence and nonexistence of a global solution for coupled nonlinear wave equations with damping and source, Nonlinear Anal., 72(11) (2010), 3969-3975.
• [2] L. Fei, G. Hongjun, Global nonexistence of positive initial-energy solutions for coupled nonlinear wave equations with damping and source terms, Abstr. Appl. Anal., (2011) 1-14.
• [3] E. Pişkin, N. Polat, Global existence, decay and blowup solution for coupled nonlinearwave equations with damping and source terms, Turk. J. Math., 37 (2013), 633-651.
• [4] R.A. Adams, J.J.F. Fournier, Sobolev Spaces, Academic Press, 2003.
• [5] A. Peyravi, Lower bounds of blow up time for a system of semilinear hyperbolic Petrovsky equations, Acta Math. Sci. 36B(3) (2016), 683-688.
• [6] E. Pişkin, Lower bounds for blow up time of coupled nonlinear Klein-Gordon equations, Gulf Journal of Mathematics, 5(2) (2017), 56-61.
• [7] N. Mezaour, E. Pişkin, Decay rate and blow up solutions for coupled quasilinear system, Boletin de la Sociedad Matematica Mexicana. (in press)