Decay of solutions for a dissipative higher-order Boussinesq system on a periodic domain

George J. Bautista; Ademir F. Pazoto

doi:10.3934/cpaa.2020035

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2020, Volume 19, Issue 2: 747-769. Doi: 10.3934/cpaa.2020035

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Decay of solutions for a dissipative higher-order Boussinesq system on a periodic domain

George J. Bautista^1, and
Ademir F. Pazoto^2, ,

1.
Universidad Privada del Norte, Campus Breña, Av. Tingo María 1122, Lima, Peru
2.
Institute of Mathematics, Federal University of Rio de Janeiro, P.O. Box 68530, CEP 21941-909, Rio de Janeiro, RJ, Brazil

^* Corresponding author
^* Corresponding author

Received: October 2018

Revised: July 2019

Published: October 2019

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Abstract

In this paper we are concerned with a Boussinesq system for small-amplitude long waves arising in nonlinear dispersive media. Considerations will be given for the global well-posedness and the time decay rates of solutions when the model is posed on a periodic domain and a general class of damping operator acts in each equation. By means of spectral analysis and Fourier expansion, we prove that the solutions of the linearized system decay uniformly or not to zero, depending on the parameters of the damping operators. In the uniform decay case, the result is extended for the full system.

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Mathematics Subject Classification: Primary: 93D15, 35Q53; Secondary: 42A16.

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References

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