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

Yıl 2020, Cilt: 3 Sayı: 2, 222 - 226, 28.12.2020

Erhan Pişkin , Fatma Ekinci

Öz

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.

Anahtar Kelimeler

General decay , Viscoelastic equations , Degenerate damping terms , Quasilinear equations

Kaynakça

• 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.