Blow up of the solutions for the Petrovsky equation with fractional damping terms

Erhan Pis¸kin; Turgay Uysal

doi:10.26637/MJM0601/0013

Abstract

In this paper, we prove a blow up result for solutions of the Petrovsky equation with fractional damping term with negative initial energy.

Keywords:

Blow up, Petrovsky equation, Fractional damping term

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Erhan Pis¸kin Department of Mathematics, Dicle University, 21280 Diyarbakır Turkey
Turgay Uysal Department of Mathematics, Dicle University, 21280 Diyarbakır Turkey.

Pages: 85-90
Date Published: 01-01-2018
Vol. 6 No. 01 (2018): Malaya Journal of Matematik (MJM)

M.R. Alaimia, N.E.Tatar, Blow up for the wave equation with a fractional damping, J. Appl. Anal. 11(1) (2005) 133-144.

W. Chen, Y. Zhou, Global nonexistence for a semilinear Petrovsky equation, Nonlinear Anal. 70 (2009) 32033208 .

S. Chen, R. Triggiani, Proof of extension of two conjectures on structural damping for elastic systems: the case $1 / 2 leq alpha leq 1$, Pacific J. Math. 136 (1989) 15-55.

G. Li, Y. Sun, 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.

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

K.B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, 1974.

E. Pişkin, N. Polat, On the decay of solutions for a nonlinear Petrovsky equation, Math. Sci. Letters, 3(1) (2014) 43-47.

I.Podlubny, Fractional Differential Equations, Math. Sci. Engrg. 198, Academic Press, San Diago, CA, 1999.

N.E. Tatar, A wave equation with fractional damping, Z. Anal. Anw. 22(3) (2003) 609-617.

N.E. Tatar, A blow up result for a fractionally damped wave equation, NoDEA, 12 (2005) 215-226.

S.T. Wu, 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.