TY - JOUR
TI - Variational principle of the 2-D steady-state convection-diffusion equation with fractal derivatives
AU - Li Xiumei
AU - Ling Weiwei
AU - Xiao Wenbo
AU - Zhan Zhiliang
AU - Zou Feng
JN - Thermal Science
PY - 2023
VL - 27
IS - 3
SP - 2049
EP - 2055
PT - Article
AB - The convection-diffusion equation describes a convection and diffusion  process, which is the cornerstone of electrochemistry. The process always  takes place in a porous medium or on an uneven boundary, and an abnormal  diffusion occurs, which will lead to deviations in prediction of the  convection-diffusion process. To overcome the problem, a fractal  modification is suggested to deal with the “abnormal” problem, and a 2-D  steady-state convection-diffusion equation with fractal derivatives in the  fractal space is established. Furthermore, its fractal variational principle  is obtained by the semi-inverse method. The fractal variational formula can  not only provide the conservation law in the fractal space in the form of  energy, but also give the possible solution structure of the equation.