RT journal article
T1 Lie Symmetries and Conservation Laws for the Viscous Cahn-Hilliard Equation
A1 Márquez Lozano, Almudena del Pilar
A1 Recio Rodríguez, Elena
A1 Gandarias Núñez, María Luz
A2 Matemáticas
K1 Cahn–Hilliard equation
K1 conservation laws
K1 exact invariant solution
K1 Lie symmetry method
K1 multi-reduction method
K1 symmetries
K1 potential systems
K1 viscous equation
AB In this paper, we study a viscous Cahn-Hilliard equation from the point of view of Lie symmetries in partial differential equations. The analysis of this equation is motivated by its applications since it serves as a model for many problems in physical chemistry, developmental biology, and population movement. Firstly, a classification of the Lie symmetries admitted by the equation is presented. In addition, the symmetry transformation groups are calculated. Afterwards, the partial differential equation is transformed into ordinary differential equations through symmetry reductions. Secondly, all low-order local conservation laws are obtained by using the multiplier method. Furthermore, we use these conservation laws to determine their associated potential systems and we use them to investigate nonlocal symmetries and nonlocal conservation laws. Finally, we apply the multi-reduction method to reduce the equation and find a soliton solution.
PB MDPI
SN 2073-8994
YR 2022
FD 2022-05
LK http://hdl.handle.net/10498/27199
UL http://hdl.handle.net/10498/27199
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-nov-2026