RT journal article
T1 Conservation laws and symmetries of radial generalized nonlinear p-Laplacian evolution equations
A1 Recio Rodríguez, Elena
A1 Anco, Stephen C.
A2 Matemáticas
K1 Nonlinear diffusion–reaction equation
K1 Conservation law
K1 Symmetry
K1 Group-invariant solution
K1 Gradient diffusivity
AB A class of generalized nonlinear p-Laplacian evolution equations is studied. Theseequations model radial diffusion–reaction processes in n ≥ 1 dimensions, where thediffusivity depends on the gradient of the flow. For this class, all local conservationlaws of low-order and all Lie symmetries are derived. The physical meaning of theconservation laws is discussed, and one of the conservation laws is used to showthat the nonlinear equation can be mapped invertibly into a linear equation bya hodograph transformation in certain cases. The symmetries are used to deriveexact group-invariant solutions from solvable three-dimensional subgroups of thefull symmetry group, which yields a direct reduction of the nonlinear equation toa quadrature. The physical and analytical properties of these exact solutions areexplored, some of which describe moving interfaces and Green’s functions.
PB Elsevier
SN 0022-247X
YR 2017
FD 2017
LK http://hdl.handle.net/10498/33279
UL http://hdl.handle.net/10498/33279
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 12-nov-2026