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

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

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)659-684
Number of pages26
JournalNonlinear Differential Equations and Applications NoDEA
Volume18
Issue number6
DOIs
StatePublished - Apr 16 2011

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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