Exponential decay of the viscoelastic wave equation of Kirchhoff type with a nonlocal dissipation

Mohamed Mellah; Ali Hakem

doi:10.24193/subbmath.2020.3.10

Authors

Mohamed Mellah
Ali Hakem

DOI:

https://doi.org/10.24193/subbmath.2020.3.10

Keywords:

Kirchhoff equation, nonlocal damping, global solution, energy decay, relaxation function

Abstract

The viscoelastic wave equation of Kirchhoff type with nonlinear and nonlocal damping is considered in a bounded domain of R^N. The existence of global solutions and decay rates of the energy are proved.

References

- F.Z. Mahdi, M. Ferhat and A. Hakem, Blow up and asymptotic behavior for a system of viscoelastic wave equations of Kirchhoff type with a delay term, Advances in the Theory of Nonlinear Analysis and its

Applications 2 (2018) No. 3, 146-167.

- Chen, H., Liu, G., 2015. Well-posedness for a class of Kirchhoff equations with damping and memory terms, IMA J. Appl. Math. 80, 1808-1836.