THERMAL SCIENCE

International Scientific Journal

Xiao-Qun Cao

,

Si-Hang Xie

,

Hong-Ze Leng

,

Wen-Long Tian

,

Jia-Le Yao

GENERALIZED VARIATIONAL PRINCIPLES FOR THE MODIFIED BENJAMIN-BONA-MAHONY EQUATION IN THE FRACTAL SPACE

ABSTRACT
Because variational principles are very important for some methods to get the numerical or exact solutions, it is very important to seek explicit variational formulations for the non-linear PDE. At first, this paper describes the modified Benjamin-Bona-Mahony equation in fractal porous media or with irregular boundaries. Then, by designing skillfully the trial-Lagrange functional, variational principles are successfully established for the modified Benjamin-Bona-Mahony equation in the fractal space, respectively. Furthermore, the obtained variational principles are proved correct by minimizing the functionals with the calculus of variations.
KEYWORDS
variational principle, modified Benjamin-Bona-Mahony equation, semi-inverse method, fractal dimension
PAPER SUBMITTED: 2023-04-11
PAPER REVISED: 2023-08-01
PAPER ACCEPTED: 2023-08-07
PUBLISHED ONLINE: 2024-05-18
DOI REFERENCE: https://doi.org/10.2298/TSCI2403341C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2024, VOLUME 28, ISSUE Issue 3, PAGES [2341 - 2349]
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Generalized variational principles for the modified Benjamin-Bona-Mahony equation in the fractal space

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence