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

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

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.

___

  • [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)