Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis

[摘要] 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 fractionof melt. The partial differential equation depends on the permeability of themedium which is assumed to be a function of the voidage. It is shown that thepartial differential equation admits, as well as translations in time and space,other Lie point symmetries provided the permeability is either a power lawor an exponential law of the voidage or is a constant. A rarefactive solitarywave solution of the partial differential equation is derived in the form of aquadrature for the exponential law for the permeability.

[学科分类] 应用数学