Open Journal of Applied Sciences

Volume 11, Issue 7 (July 2021)

ISSN Print: 2165-3917   ISSN Online: 2165-3925

Google-based Impact Factor: 0.92  Citations  h5-index & Ranking

The Family of Global Attractors for a Generalized Kirchhoff Equations

HTML  XML Download Download as PDF (Size: 389KB)  PP. 789-806  
DOI: 10.4236/ojapps.2021.117058    151 Downloads   561 Views  

ABSTRACT

This paper deals with the existence and uniqueness of solutions of generalized Kirchhoff equations and the family of global attractors for the equation and its dimension estimation. First, the stress term of Kirchhoff equation is properly assumed. When certain conditions are met between the order m and the degree p of Banach space , the existence and uniqueness of the solution of equation are obtained by a prior estimation and Galerkin’s method; Then, the bounded absorption set is obtained by prior estimation, and it is proved that the solution semigroup generated by the equation has a family of global attractors in phase space by using Rellich-Kondrachov compact embedding theorem. Further, the equation is linearized and rewritten into a first-order variational equation, and it is proved that the solution semigroup is Fréchet differentiable on ; Finally, the upper bound of Hausdorff dimension and Fractal dimension of is estimated, and the Hausdorff dimension and Fractal dimension are finite.

Share and Cite:

Lin, G. and Liu, X. (2021) The Family of Global Attractors for a Generalized Kirchhoff Equations. Open Journal of Applied Sciences, 11, 789-806. doi: 10.4236/ojapps.2021.117058.

Cited by

No relevant information.

Journals Menu
Follow SCIRP
Contact us
+1 323-425-8868
customer@scirp.org
WhatsApp +86 18163351462(WhatsApp)
Click here to send a message to me 1655362766
Paper Publishing WeChat

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.