Large-Time Behavior of a Linear Boussinesq System for the Water Waves

Bautista, George J.; Pazoto, Ademir F.

doi:10.1007/s10884-018-9689-4

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…Our analysis were inspired by an earlier work on the subject [15] and aims to add considerably to the conclusions drawn therein (see also [2]). By using the same approach the authors derived similar results when the parameters given in (2) are such that a = c = b…”

Section: Decay Of Solutions For a Dissipative Boussinesq System 749mentioning

confidence: 99%

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

Bautista¹,

Pazoto²

2020

Communications on Pure &Amp; Applied Analysis

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In this paper we are concerned with a Boussinesq system for smallamplitude 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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Section: Decay Of Solutions For a Dissipative Boussinesq System 749mentioning

confidence: 99%

“…In this paper, our purpose is to investigate such questions by considering a general class of damping operator with nonnegative symbol. Considerations will be given to the Boussinesq system, posed on a periodic domain, when the parameters in (2) are such that a 2 = c 2 = 0. More precisely, we consider the model…”

mentioning

confidence: 99%

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

Bautista¹,

Pazoto²

2020

Communications on Pure &Amp; Applied Analysis

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“…Our proofs rely on the approach developed in [20] to study similar problems for the scalar BBM equation and [4,22] for the BBM-type systems.…”

Section: Introductionmentioning

confidence: 99%

Long-time asymptotics of a linear higher-order water wave model

Bautista,

Sierra

2023

Preprint

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A higher-order BBM equation is considered with selected internal and boundary conditions as feedback laws to dissipate the energy. We propose several dissipation mechanisms leading to equations for which one has both, the global existence of solutions and non-increasing energy. Following the analysis developed in \cite{rosier} we prove that all the trajectories are attracted by the origin or the mean of initial data provided that the unique continuation property of weak solutions holds. MSC: Primary: 35A01, 3AQ02, 35B40, 35B60, 35B65. Secondary: 35B10, 35B35

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Asymptotic behavior of a linear higher-order BBM-system with damping

Fonseca

Pazoto²

2022

Z. Angew. Math. Phys.

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Large-Time Behavior of a Linear Boussinesq System for the Water Waves

Cited by 4 publications

References 10 publications

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

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

Long-time asymptotics of a linear higher-order water wave model

Asymptotic behavior of a linear higher-order BBM-system with damping

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