Robustness of exponentially κ-dissipative dynamical systems with perturbations

Jin Zhang; Yonghai Wang; Chengkui Zhong

doi:10.3934/dcdsb.2017198

Article Contents

2017, Volume 22, Issue 10: 3875-3890. Doi: 10.3934/dcdsb.2017198

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Robustness of exponentially κ-dissipative dynamical systems with perturbations

1.
Department of Mathematics, College of Science, Hohai University, Nanjing, 210098, China
2.
Department of Applied Mathematics, Donghua University, Shanghai, 201620, China
3.
Department of Mathematics, Nanjing University, Nanjing, 210093, China

* Corresponding author: Yonghai Wang
* Corresponding author: Yonghai Wang

Received: September 2016

Revised: April 2017

Published online: July 2017

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Abstract

We study the robustness of exponentially $κ$-dissipative dynamical systems with perturbed parameters $\varepsilon∈ E(\subset\mathbb{R})$. In particular, under some proper assumptions, we will construct a family of compact sets $\{\mathcal A_\varepsilon\}_{\varepsilon∈ E}$, which is positive invariant, uniformly exponentially attracting and equi-continuous. At last, an application to a Kirchhoff wave model is given.

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Mathematics Subject Classification: Primary:37L05, 35B40;Secondary:35B41.

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