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Lie symmetries and conservation laws of the Fokker‐Planck equation with power diffusion
Author(s) -
Zhang ZhiYong,
Zheng Jia,
Guo LeiLei,
Wu HongFeng
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6582
Subject(s) - conservation law , mathematics , fokker–planck equation , homogeneous space , partial differential equation , symmetry (geometry) , law , diffusion equation , noether's theorem , heat equation , power law , mathematical analysis , geometry , statistics , economy , political science , economics , service (business)
We concentrate on Lie symmetries and conservation laws of the Fokker‐Planck equation with power diffusion describing the growth of cell populations. First, we perform a complete symmetry classification of the equation, and then we find some interesting similarity solutions by means of the symmetries and the variable coefficient heat equation. Local dynamical behaviors are analyzed via the solutions for the growing cell populations. Second, we show that the conservation law multipliers of the equation take the form Λ=Λ( t , x , u ), which satisfy a linear partial differential equation, and then give the general formula of conservation laws. Finally, symmetry properties of the conservation law are investigated and used to construct conservation laws of the reduced equations.