General decay of solutions of a nonlinear system of viscoelastic wave equations. (English) Zbl 1246.35040
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, the authors 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 [S. A. Messaoudi and N.-E. Tatar, Appl. Anal. 87, No. 3, 247–263 (2008; Zbl 1139.35320); W. Liu, Nonlinear Anal., Theory Methods Appl. 71, No. 5–6, A, 2257–2267 (2009; Zbl 1167.35318)] in which only the exponential and polynomial decay rates are considered.
This result improves many results in the literature, such as the ones in [S. A. Messaoudi and N.-E. Tatar, Appl. Anal. 87, No. 3, 247–263 (2008; Zbl 1139.35320); W. Liu, Nonlinear Anal., Theory Methods Appl. 71, No. 5–6, A, 2257–2267 (2009; Zbl 1167.35318)] in which only the exponential and polynomial decay rates are considered.
Reviewer: Shun-Tang Wu (Zhonghe)
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35L53 | Initial-boundary value problems for second-order hyperbolic systems |
| 35L70 | Second-order nonlinear hyperbolic equations |
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