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Year 2020, Volume: 3 Issue: 1, 55 - 62, 15.12.2020

Abstract

References

  • 1 E. Pişkin, F. Ekinci, General decay and blowup of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms, Math. Method Appl. Sci. 42(16) (2019), 1-21.
  • 2 S.T. Wu, General decay of solutions for a nonlinear system of viscoelastic wave equations with degenerate damping and source terms, J. Math. Anal. Appl. 406 (2013), 34-48.
  • 3 E. Pişkin, F. Ekinci, K. Zennir, Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms, Theoret. Appl. Mech. 47(1) (2020), 123-154.
  • 4 B. Feng, Y. Qin, M. Zhang, General decay for a system of nonlinear viscoelastic wave equations with weak damping, Bound. Value Probl. 146 (2012), 1-11.
  • 5 X.S. Han, M.X. Wang, Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source, Nonlinear Anal. TMA 71 (2009) 5427-5450.
  • 6 B. Said-Houari, S.A. Messaoudi, A. Guesmia, General decay of solutions of a nonlinear system of viscoelastic wave equations, NoDEA 18 (2011), 659-684.
  • 7 S.A. Messaoudi, B. S. Houari, Global nonexistence of positive initial-energy solutions of a system of nonlinear viscoelastic wave equations with damping and source terms, J. Math. Anal. Appl. 365 (2010), 277-287.
  • 8 E. Pişkin, Global nonexistence of solutions for a system of viscoelastic wave equations with weak damping terms, Malaya J. Mat. 3(2) (2015), 168-174 .
  • 9 E. Pişkin, A lower bound for the blow up time of a system of viscoelastic wave equations with nonlinear damping and source terms, J. Nonlinear Funct. Anal. 2017 (2017), 1-9.
  • 10 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, Nonliner Studies 19(4) (2012), 523-535.
  • 11 K. Zennir, Growth of solutions to system of nonlinear wave equations with degenerate damping and strong sources, Nonlinear Anal. Appl. (2013), 1-11.
  • 12 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 Anal. TMA 72 (2010), 2658-2683.
  • 13 E. Vitillaro Global nonexistence theorems for a class of evolution equations with dissipation, Arch. Ration. Mech. Anal. 149 (1999), 155-182.

Local Existence and Blow Up of Solutions for a Coupled Viscoelastic Kirchhoff-Type Equations with Degenerate Damping

Year 2020, Volume: 3 Issue: 1, 55 - 62, 15.12.2020

Abstract

In this paper, we consider the initial boundary value problem of a coupled viscoelastic Kirchhofftype equations with degenerate damping. Firstly, we prove a local existence theorem by using the Faedo-Galerkin approximations. Then, we study blow up of solutions when initial energy is possitive.

References

  • 1 E. Pişkin, F. Ekinci, General decay and blowup of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms, Math. Method Appl. Sci. 42(16) (2019), 1-21.
  • 2 S.T. Wu, General decay of solutions for a nonlinear system of viscoelastic wave equations with degenerate damping and source terms, J. Math. Anal. Appl. 406 (2013), 34-48.
  • 3 E. Pişkin, F. Ekinci, K. Zennir, Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms, Theoret. Appl. Mech. 47(1) (2020), 123-154.
  • 4 B. Feng, Y. Qin, M. Zhang, General decay for a system of nonlinear viscoelastic wave equations with weak damping, Bound. Value Probl. 146 (2012), 1-11.
  • 5 X.S. Han, M.X. Wang, Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source, Nonlinear Anal. TMA 71 (2009) 5427-5450.
  • 6 B. Said-Houari, S.A. Messaoudi, A. Guesmia, General decay of solutions of a nonlinear system of viscoelastic wave equations, NoDEA 18 (2011), 659-684.
  • 7 S.A. Messaoudi, B. S. Houari, Global nonexistence of positive initial-energy solutions of a system of nonlinear viscoelastic wave equations with damping and source terms, J. Math. Anal. Appl. 365 (2010), 277-287.
  • 8 E. Pişkin, Global nonexistence of solutions for a system of viscoelastic wave equations with weak damping terms, Malaya J. Mat. 3(2) (2015), 168-174 .
  • 9 E. Pişkin, A lower bound for the blow up time of a system of viscoelastic wave equations with nonlinear damping and source terms, J. Nonlinear Funct. Anal. 2017 (2017), 1-9.
  • 10 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, Nonliner Studies 19(4) (2012), 523-535.
  • 11 K. Zennir, Growth of solutions to system of nonlinear wave equations with degenerate damping and strong sources, Nonlinear Anal. Appl. (2013), 1-11.
  • 12 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 Anal. TMA 72 (2010), 2658-2683.
  • 13 E. Vitillaro Global nonexistence theorems for a class of evolution equations with dissipation, Arch. Ration. Mech. Anal. 149 (1999), 155-182.
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Erhan Pişkin

Fatma Ekinci

Publication Date December 15, 2020
Acceptance Date October 4, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Pişkin, E., & Ekinci, F. (2020). Local Existence and Blow Up of Solutions for a Coupled Viscoelastic Kirchhoff-Type Equations with Degenerate Damping. Conference Proceedings of Science and Technology, 3(1), 55-62.
AMA Pişkin E, Ekinci F. Local Existence and Blow Up of Solutions for a Coupled Viscoelastic Kirchhoff-Type Equations with Degenerate Damping. Conference Proceedings of Science and Technology. December 2020;3(1):55-62.
Chicago Pişkin, Erhan, and Fatma Ekinci. “Local Existence and Blow Up of Solutions for a Coupled Viscoelastic Kirchhoff-Type Equations With Degenerate Damping”. Conference Proceedings of Science and Technology 3, no. 1 (December 2020): 55-62.
EndNote Pişkin E, Ekinci F (December 1, 2020) Local Existence and Blow Up of Solutions for a Coupled Viscoelastic Kirchhoff-Type Equations with Degenerate Damping. Conference Proceedings of Science and Technology 3 1 55–62.
IEEE E. Pişkin and F. Ekinci, “Local Existence and Blow Up of Solutions for a Coupled Viscoelastic Kirchhoff-Type Equations with Degenerate Damping”, Conference Proceedings of Science and Technology, vol. 3, no. 1, pp. 55–62, 2020.
ISNAD Pişkin, Erhan - Ekinci, Fatma. “Local Existence and Blow Up of Solutions for a Coupled Viscoelastic Kirchhoff-Type Equations With Degenerate Damping”. Conference Proceedings of Science and Technology 3/1 (December 2020), 55-62.
JAMA Pişkin E, Ekinci F. Local Existence and Blow Up of Solutions for a Coupled Viscoelastic Kirchhoff-Type Equations with Degenerate Damping. Conference Proceedings of Science and Technology. 2020;3:55–62.
MLA Pişkin, Erhan and Fatma Ekinci. “Local Existence and Blow Up of Solutions for a Coupled Viscoelastic Kirchhoff-Type Equations With Degenerate Damping”. Conference Proceedings of Science and Technology, vol. 3, no. 1, 2020, pp. 55-62.
Vancouver Pişkin E, Ekinci F. Local Existence and Blow Up of Solutions for a Coupled Viscoelastic Kirchhoff-Type Equations with Degenerate Damping. Conference Proceedings of Science and Technology. 2020;3(1):55-62.