TY - JOUR
TI - Generalized variational principles for the modified Benjamin-Bona-Mahony equation in the fractal space
AU - Cao Xiao-Qun
AU - Xie Si-Hang
AU - Leng Hong-Ze
AU - Tian Wen-Long
AU - Yao Jia-Le
JN - Thermal Science
PY - 2024
VL - 28
IS - 3
SP - 2341
EP - 2349
PT - Article
AB - 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.