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Dergiler / Conference Proceedings of Science and Technology / 2020 / Cilt: 3 Sayı: 2

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

Erhan Pişkin(DICLE UNIVERSITY)
Fatma Ekinci(Dicle üniversitesi)
Sayfa
222–226
Yayın Tarihi
2020-12-28
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

This work generalizes and improves earlier results in the literature.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this work, we investigate a quasilinear system of two viscoelastic equations with degenarete damping, dispersion and source terms under Dirichlet boundary conditions.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:This work generalizes and improves earlier results in the literature.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:General decay · Viscoelastic equations · Degenerate damping terms

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.

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Bu Makaleye Atıf Yap

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, Cilt: 3 Sayı: 2, 222–226. https://ajindex.com/articles/984323

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Kaynakça (9)

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  2. 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. 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. 4 L. He, On decay of solutions for a system of coupled viscoelastic equations, Acta Appl Math. (167), (2020), 171-198.
  5. 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. 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. 7 Adams RA, Fournier JJF. Sobolev Spaces. Academic Press, New York, 2003.
  8. 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. 9 W. Liu, General decay and blow-up of solution for a quasilinear viscoelastic problem with nonlinear source, Nonlinear Anal. (73), (2010), 1890-1904.