an:06175775
Zbl 1266.86006
Mindu, N.; Mason, D. P.
Permeability models for magma flow through the Earth's mantle: a Lie group analysis
EN
J. Appl. Math. 2013, Article ID 258528, 8 p. (2013).
00318830
2013
j
86A99 74J35 35Q86
Summary: The migration of melt through the mantle of the Earth is governed by a third-order nonlinear partial differential equation for the voidage or volume fraction of melt. The partial differential equation depends on the permeability of the medium which is assumed to be a function of the voidage. It is shown that the partial differential equation admits, as well as translations in time and space, other Lie point symmetries provided the permeability is either a power law or an exponential law of the voidage or is a constant. A rarefactive solitary wave solution of the partial differential equation is derived in the form of a quadrature for the exponential law for the permeability.