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Research Article

Existence, blow up and growth of solutions for a coupled quasi-linear viscoelastic Petrovsky equations with degenerate damping terms

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Pages 705-733 | Received 01 Jan 2021, Published online: 16 Dec 2021

References

  • J. M. Rivera, E. C. Lapa, R. Barreto, Decay rates for viscoelastic plates with memory. Journal of elasticity, 44(1) (1996) 61-87. doi: 10.1007/BF00042192
  • F. Alabau-Boussouira, P. Cannarsa, D. Sforza, Decay estimates for the second order evolution equation with memory. Journal of Functional Analysis, 245(5) (2008) 1342-1372. doi: 10.1016/j.jfa.2007.09.012
  • S. A. Messaoudi, Global existence and nonexistence in a system of Petrovsky. Journal of Mathematical Analysis and Applications, 265(2) (2002) 296-308. doi: 10.1006/jmaa.2001.7697
  • M.M. Cavalcanti, V.N.D. Cavalcanti, J. Ferreira, Existence and uniform decay for a non-linear viscoelastic equation with strong damping. Mathematical Methods in the Applied Sciences, 24(14) (2001) 1043-1053. doi: 10.1002/mma.250
  • S. A. Messaoudi, N. E. Tatar, Global existence and asymptotic behavior for a nonlinear viscoelastic problem. Mathematical Sciences Research Journal, 7(4) (2003) 136-149.
  • F. Tahamtani, A. Pevravi, Global existence, uniform decay, and exponential growth of solutions for a system of viscoelastic Petrovsky equations. Turkish Journal of Mathematics, 38 (2014) 87-109. doi: 10.3906/mat-1212-15
  • M. A. Rammaha, S. Sakuntasathien, Global existence and blow up of solutions to systems of nonlinear wave equations with degenerate damping and source terms. Nonlinear Analysis: Theory, Methods & Applications, 72 (2010) 2658-2683.
  • A. Benaissa, D. Ouchenane, K. Zennir, Blow up of positive initial energy solutions to system of nonlinear wave equations with degenerate damping and source terms. Nonlinear Studies, 19(4) (2012) 523-535.
  • K. Zennir, Growth of solutions to system of nonlinear wave equations with degenerate damping and strong sources. Nonlinear Analysis and Application, 2013 (2013) 1-11.
  • E. Pişkin, Blow up of positive initial-energy solutions for coupled nonlinear wave equations with degenerate damping and source terms. Boundary Value Problems, 43 (2015) 1-11.
  • ST. Wu, General decay of solutions for a nonlinear system of viscoelastic wave equations with degenerate damping and source terms. Journal of Mathematical Analysis and Applications, 406 (2013) 34-48. doi: 10.1016/j.jmaa.2013.04.029
  • K. Zennir, Growth of solutions with positive initial energy to system of degeneratly damped wave equations with memory. Lobachevskii Journal of Mathematics, 35(2) (2014) 147-156. doi: 10.1134/S1995080214020139
  • E. Pişkin, F. Ekinci, K. Zennir, Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms. Theoretical and Applied Mechanics, 47(1) (2020) 123-154. doi: 10.2298/TAM200428008P
  • E. Pişkin, F. Ekinci, Nonexistence of global solutions for coupled Kirchhoff-type equations with degenerate damping terms. Journal of Nonlinear Functional Analysis 2018 (2018), Article ID 48.
  • RA. Adams, JJF. Fournier, Sobolev Spaces. Academic Press, New York, 2003.
  • S. A. Messaoudi, Blow up in a nonlinearly damped wave equation. Mathematische Nachrichten, 231 (2001) 105-111. doi: 10.1002/1522-2616(200111)231:1<105::AID-MANA105>3.0.CO;2-I
  • B. Said-Houari, S.A. Messaoudi, A. Guesmia, General decay of solutions of a nonlinear system of viscoelastic wave equations. Nonlinear Differential Equations and Applications NoDEA, 18 (2011) 659–684. doi: 10.1007/s00030-011-0112-7
  • Y. Ye, Existence and Asymptotic Behavior of Global Solutions bf for Some Nonlinear Petrovsky System. Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, 59(107) (2016) 389-398.
  • E. Pişkin, F. Ekinci, General decay and blow up of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms. Mathematical Methods in the Applied Sciences, 42(16) (2019) 5468-5488. doi: 10.1002/mma.5429

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