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

被引：1
|
作者：
Cao, Xiao-Qun [1 ,2 ]
Xie, Si -Hang [1 ]
Leng, Hong-Ze [1 ]
Tian, Wen -Long [2 ]
Yao, Jia-Le [1 ]
机构：
[1] Natl Univ Def Technol, Coll Meteorol & Oceanog, Changsha, Peoples R China
[2] Natl Univ Def Technol, Coll Comp, Changsha, Peoples R China
来源：
THERMAL SCIENCE | 2024年 / 28卷 / 3A期
基金：
中国国家自然科学基金; 国家重点研发计划;
关键词：
variational principle; modified Benjamin-Bona-Mahony equation; semi-inverse method; fractal dimension; ITERATION METHOD; DIFFERENTIAL-EQUATIONS; CALCULUS; APPROXIMATIONS; CHALLENGES; PROMISES;
D O I：
10.2298/TSCI2403341C
中图分类号：
O414.1 [热力学];
学科分类号：
摘要：
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.
引用
收藏
页码：2341 / 2349
页数：9
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