The asymptotic behaviors of solutions for higher-order (m 1, m 2)-coupled Kirchhoff models with nonlinear strong damping-Reference-Cited by-同舟云学术

The asymptotic behaviors of solutions for higher-order (m ₁, m ₂)-coupled Kirchhoff models with nonlinear strong damping

Published:2023-01-01 Issue:1 Volume:56 Page:
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Lv Penghui¹,Lin Guoguang²,Lv Xiaojun¹

Affiliation:

1. Applied Technology College of Soochow University , Suzhou , Jiangsu, 215325 , China

2. School of Mathematics and Statistics , Yunnan University , Kunming , Yunnan, 650500 , China

Abstract

Abstract The Kirchhoff model is derived from the vibration problem of stretchable strings. This article focuses on the long-time dynamics of a class of higher-order coupled Kirchhoff systems with nonlinear strong damping. The existence and uniqueness of the solutions of these equations in different spaces are proved by prior estimation and the Faedo-Galerkin method. Subsequently, the family of global attractors of these problems is proved using the compactness theorem. In this article, we systematically propose the definition and proof process of the family of global attractors and enrich the related conclusions of higher-order coupled Kirchhoff models. The conclusions lay a theoretical foundation for future practical applications.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2022-0197/pdf

Reference21 articles.

1. I. Chueshov, Long-time dynamics of Kirchhoff wave models with strong nonlinear damping, J. Differ. Equations 252 (2012), no. 2, 1229–1262, DOI: https://doi.org/10.1016/j.jde.2011.08.022.

2. G. Lin, P. Lv, and R. Lou, Exponential attractors and inertial manifolds for a class of nonlinear generalized Kirchhoff-Boussinesq model, Far East J. Math. Sci. 101 (2017), no. 9, 1913–1945, DOI: https://doi.org/10.17654/MS101091913.

3. M. Ghisi and M. Gobbino, Kirchhoff equations with strong damping, J. Evol. Equ. 16 (2016), no. 2, 441–482, DOI: https://doi.org/10.1007/s00028-015-0308-0.

4. M. Nakao, An attractor for a nonlinear dissipative wave equation of Kirchhoff type, J. Math. Anal. Appl. 353 (2008), no. 2, 652–659, DOI: https://doi.org/10.1016/j.jmaa.2008.09.010.

5. Y. Cao and Q. Zhao, Asymptotic behavior of global solutions to a class of mixed pseudo-parabolic Kirchhoff equations, Appl. Math. Lett. 118 (2021), 107119, DOI: https://doi.org/10.1016/J.AML.2021.107119.

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