TY - JOUR
T1 - General decay of solutions of a nonlinear system of viscoelastic wave equations
AU - Said-Houari, Belkacem
AU - Messaoudi, Salim A.
AU - Guesmia, Aïssa
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2011/4/16
Y1 - 2011/4/16
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/561755
UR - http://link.springer.com/10.1007/s00030-011-0112-7
UR - http://www.scopus.com/inward/record.url?scp=81455135489&partnerID=8YFLogxK
U2 - 10.1007/s00030-011-0112-7
DO - 10.1007/s00030-011-0112-7
M3 - Article
SN - 1021-9722
VL - 18
SP - 659
EP - 684
JO - Nonlinear Differential Equations and Applications NoDEA
JF - Nonlinear Differential Equations and Applications NoDEA
IS - 6
ER -