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

页码：2341 / 2349

页数：9

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