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On the wave equations with a dissipation anda source of cubic convolution type in Rn

Tatar N.-e.

Demonstratio Mathematica

2004

Vol. 37, nr 3

543--555

We study the interaction between a dissipative term and a source term of cubic convolution type for the wave equation in Rn. These terms have both the same form and involve convolutions with a singular kernel. The investigation will depend on the coefficient of the source term which is a functions of the time variable. Some results on the boundedness of the solutions are proved. Moreover, we establish an asymptotic stability result.

Uniform decay rates for solutions to a structural acoustics model with nonlinear dissipation

Avalos G., Lasiecka I.

Applied Mathematics and Computer Science

1998

Vol. 8, no 2

287-312

In this work, the asymptotic behavior of solutions to a coupled hyperbolic/parabolic-like system is investigated. It is shown that with both components of the equation being subjected to nonlinear damping (boundary damping for the wave component, interior for the beam), a global uniform stability is attained for all (weak) solutions.