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Year 2020, Volume: 3 Issue: 2, 222 - 226, 28.12.2020

Abstract

References

  • 1 ST. Wu, General decay of solutions for a viscoelastic equation with nonlinear damping and source terms, Acta Math Sci., (318), (2011), 1436-1448.
  • 2 ST. Wu, General decay of energy for a viscoelastic equation with damping and source terms, Taiwan J Math., 16 (1), (2012), 113-128.
  • 3 L. He, On decay and blow-up of solutions for a system of equations, Appl Anal., (2019), 1-30. Doi: 10.1080/00036811.2019.1689562.
  • 4 L. He, On decay of solutions for a system of coupled viscoelastic equations, Acta Appl Math. (167), (2020), 171-198.
  • 5 E. Pişkin, F. Ekinci, General decay and blow-up of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms, Math Meth Appl Sci., 42 (16), (2019), 5468-5488.
  • 6 ST. 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.
  • 7 Adams RA, Fournier JJF. Sobolev Spaces. Academic Press, New York, 2003.
  • 8 B. Said-Houari, SA. Messaoudi, A. Guesmia, General decay of solutions of a nonlinear system of viscoelastic wave equations, NoDEA Nonlinear Differential Equations Appl., (2011), (18), 659-684.
  • 9 W. Liu, General decay and blow-up of solution for a quasilinear viscoelastic problem with nonlinear source, Nonlinear Anal. (73), (2010), 1890-1904.

Global Existence and General Decay of Solutions for Quasilinear System with Degenerate Damping Terms

Year 2020, Volume: 3 Issue: 2, 222 - 226, 28.12.2020

Abstract

In this work, we investigate a quasilinear system of two viscoelastic equations with degenarete damping, dispersion and source terms under Dirichlet boundary conditions. Under suitable conditions on the relaxation function $h_{i}$ $\left( i=1,2\right)$ and initial data, we establish global existence and general decay results. This work generalizes and improves earlier results in the literature.

References

  • 1 ST. Wu, General decay of solutions for a viscoelastic equation with nonlinear damping and source terms, Acta Math Sci., (318), (2011), 1436-1448.
  • 2 ST. Wu, General decay of energy for a viscoelastic equation with damping and source terms, Taiwan J Math., 16 (1), (2012), 113-128.
  • 3 L. He, On decay and blow-up of solutions for a system of equations, Appl Anal., (2019), 1-30. Doi: 10.1080/00036811.2019.1689562.
  • 4 L. He, On decay of solutions for a system of coupled viscoelastic equations, Acta Appl Math. (167), (2020), 171-198.
  • 5 E. Pişkin, F. Ekinci, General decay and blow-up of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms, Math Meth Appl Sci., 42 (16), (2019), 5468-5488.
  • 6 ST. 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.
  • 7 Adams RA, Fournier JJF. Sobolev Spaces. Academic Press, New York, 2003.
  • 8 B. Said-Houari, SA. Messaoudi, A. Guesmia, General decay of solutions of a nonlinear system of viscoelastic wave equations, NoDEA Nonlinear Differential Equations Appl., (2011), (18), 659-684.
  • 9 W. Liu, General decay and blow-up of solution for a quasilinear viscoelastic problem with nonlinear source, Nonlinear Anal. (73), (2010), 1890-1904.
There are 9 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Erhan Pişkin

Fatma Ekinci

Publication Date December 28, 2020
Acceptance Date December 12, 2020
Published in Issue Year 2020 Volume: 3 Issue: 2

Cite

APA Pişkin, E., & Ekinci, F. (2020). Global Existence and General Decay of Solutions for Quasilinear System with Degenerate Damping Terms. Conference Proceedings of Science and Technology, 3(2), 222-226.
AMA Pişkin E, Ekinci F. Global Existence and General Decay of Solutions for Quasilinear System with Degenerate Damping Terms. Conference Proceedings of Science and Technology. December 2020;3(2):222-226.
Chicago Pişkin, Erhan, and Fatma Ekinci. “Global Existence and General Decay of Solutions for Quasilinear System With Degenerate Damping Terms”. Conference Proceedings of Science and Technology 3, no. 2 (December 2020): 222-26.
EndNote Pişkin E, Ekinci F (December 1, 2020) Global Existence and General Decay of Solutions for Quasilinear System with Degenerate Damping Terms. Conference Proceedings of Science and Technology 3 2 222–226.
IEEE E. Pişkin and F. Ekinci, “Global Existence and General Decay of Solutions for Quasilinear System with Degenerate Damping Terms”, Conference Proceedings of Science and Technology, vol. 3, no. 2, pp. 222–226, 2020.
ISNAD Pişkin, Erhan - Ekinci, Fatma. “Global Existence and General Decay of Solutions for Quasilinear System With Degenerate Damping Terms”. Conference Proceedings of Science and Technology 3/2 (December 2020), 222-226.
JAMA Pişkin E, Ekinci F. Global Existence and General Decay of Solutions for Quasilinear System with Degenerate Damping Terms. Conference Proceedings of Science and Technology. 2020;3:222–226.
MLA Pişkin, Erhan and Fatma Ekinci. “Global Existence and General Decay of Solutions for Quasilinear System With Degenerate Damping Terms”. Conference Proceedings of Science and Technology, vol. 3, no. 2, 2020, pp. 222-6.
Vancouver Pişkin E, Ekinci F. Global Existence and General Decay of Solutions for Quasilinear System with Degenerate Damping Terms. Conference Proceedings of Science and Technology. 2020;3(2):222-6.