General decay of solutions of a nonlinear system of viscoelastic wave equations

Said-Houari, Belkacem; Messaoudi, Salim A.; Guesmia, Aïssa

General decay of solutions of a nonlinear system of viscoelastic wave equations

Type

Article

Authors

Said-Houari, Belkacem
Messaoudi, Salim A.
Guesmia, Aïssa

KAUST Department

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Online Publication Date

2011-04-16

Print Publication Date

2011-12

Date

2011-04-16

Abstract

This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247-263, 2008) and Liu (Nonlinear Anal. 71:2257-2267, 2009) in which only the exponential and polynomial decay rates are considered. © 2011 Springer Basel AG.

Citation

Said-Houari, B., Messaoudi, S. A., & Guesmia, A. (2011). General decay of solutions of a nonlinear system of viscoelastic wave equations. Nonlinear Differential Equations and Applications NoDEA, 18(6), 659–684. doi:10.1007/s00030-011-0112-7