Dynamical behavior of Benjamin-Bona-Mahony system with finite distributed delay in 3D

Lingrui Zhang; Xue-zhi Li; Keqin Su; Lingrui Zhang; Xue-zhi Li; Keqin Su

doi:10.3934/era.2023348

Electronic Research Archive

2023, Volume 31, Issue 11: 6881-6897. doi: 10.3934/era.2023348

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Research article

Dynamical behavior of Benjamin-Bona-Mahony system with finite distributed delay in 3D

1.
Department of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
2.
College of Information and Management Science, Henan Agricultural University, Zhengzhou 450046, China

Received: 18 August 2023 Revised: 04 October 2023 Accepted: 08 October 2023 Published: 26 October 2023

We study the Benjamin-Bona-Mahony model with finite distributed delay in 3D, which depicts the dispersive impact of long waves. Based on the well-posedness of model, the family of pullback attractors for the evolutionary processes generated by a global weak solution has been obtained, which is unique and minimal, via verifying asymptotic compactness in functional space with delay $ C_V $ and topological space $ V\times C_V $, where the energy equation method and a retarded Gronwall inequality are utilized.
- Benjamin-Bona-Mahony system,
- distributed delay,
- pullback attractor
Citation: Lingrui Zhang, Xue-zhi Li, Keqin Su. Dynamical behavior of Benjamin-Bona-Mahony system with finite distributed delay in 3D[J]. Electronic Research Archive, 2023, 31(11): 6881-6897. doi: 10.3934/era.2023348

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Abstract

We study the Benjamin-Bona-Mahony model with finite distributed delay in 3D, which depicts the dispersive impact of long waves. Based on the well-posedness of model, the family of pullback attractors for the evolutionary processes generated by a global weak solution has been obtained, which is unique and minimal, via verifying asymptotic compactness in functional space with delay $ C_V $ and topological space $ V\times C_V $, where the energy equation method and a retarded Gronwall inequality are utilized.

References

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