Blow-up result in a Cauchy problem for the nonlinear viscoelastic Petrovsky equation


  • Erhan PiÅŸkin Dicle University





Blow Up, Cauchy Problem, Nonlinear Viscoelastic Petrovsky Equation.


In this paper, we consider a Cauchy problem for the nonlinear viscoelastic Petrovsky equation. We obtain the blow up of solutions by applying a lemma due to Zhou.


[1] N. E. Amroun and A. Benaissa, Global existence and energy decay of solutions to a Petrovsky equation with general nonlinear dissipation and source term, Georgian Math J, 13(3) (2006) 397-410.

[2] W. Chen and Y. Zhou, Global nonexistence for a semilinear Petrovsky equation, Nonlinear Analysis, 70 (2009) 3203-3208.

[3] A. Guesmia, Existence globale ET stabilisation interne nonlin’eaire d'un syst`eme dePetrovsky, Bulletin of the Belgian Mathematical Society, 5(4) (1998) 583-594.

[4] M. Kafini and M.I. Mustafa, Blow up result in a Cauchy viscoelastic problem with strong damping and dispersive, Nonlinear Analysis: RWA, 20 (2014) 14-20.

[5] G. Li, Y. Sun and W. Liu, On asymptotic behavior and blow-up of solutions for a nonlinear viscoelastic Petrovsky equation with positive initial energy, J Function Spaces Appl, (2013) 1-7.

[6] G. Li, Y. Sun and W. Liu, Global existence and blow up of solutions for a strongly damped Petrovsky system with nonlinear damping, Appl. Anal, 91(3) (2012) 575-586.

[7] S.A. Messaoudi, Global existence and nonexistence in a system of Petrovsky, J Math Anal Appl, 265(2) (2002) 296-308.

[8] E. PiÅŸkin and N. Polat, on the decay of solutions for a nonlinear Petrovsky equation, Mathematical Sciences Letters, 3(1) (2014) 43-47.

[9] S.T. Wu and L.Y. Tsai, on global solutions and blow-up of solutions for a nonlinearly damped Petrovsky system, Taiwanese J. Math. 13 (2A) (2009) 545-558.

[10] Y. Zhou, A blow-up result for a nonlinear wave equation with damping and vanishing initial energy in, Appl. Math. Lett, 18 (2005) 281-286.

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