Rarefactive solitary waves in two-phase fluid flow of compacting media
type: Item
instance of: scholarly article
title: Rarefactive solitary waves in two-phase fluid flow of compacting media
zbMATH Open document ID: 0761.76097
DOI: 10.1016/0165-2125(92)90054-6
author: S. Singh
published in: Wave Motion
publication date: 1993-04-01T00:00:00Z
review text: Rarefactive solitary wave solutions of a third order nonlinear partial differential equation derived by \textit{D. R. Scott} and \textit{D. J. Stevenson} [Geophys. Res. Lett. 11, No. 11, 1161-1164 (1984)] to describe the one-dimensional migration of melt under the action of gravity through the Earth's mantle are investigated. The partial differential equation contains two parameters, \(n\) and \(m\), which are the exponents in power laws relating, respectively, the permeability of the medium and the bulk and shear viscosities of the solid matrix to the voidage. It is proved that, for any value of \(m\), rarefactive solitary wave solutions satisfying certain physically reasonable boundary conditions always exist if \(n>1\) but do not exist if \(0\leq n\leq 1\). It is also proved that the speed of the solitary wave is an increasing function of the amplitude of the wave. Six new exact rarefactive solitary wave solutions, four of which are expressed in terms of elementary functions and two in terms of elliptic integrals, are derived.
Mathematics Subject Classification ID: 76T99
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 86A60
zbMATH DE Number: 147210
zbMATH Keywords: one-dimensional migration of melt
zbMATH Keywords: gravity
zbMATH Keywords: Earth's mantle
zbMATH Keywords: new exact rarefactive solitary wave solutions
MaRDI profile type: Publication
full work available at URL: 0165-2125(92)90054-6
OpenAlex ID: W1998107314
cites work: A mathematical model of magma transport in the asthenosphere
cites work: Nonlinear waves in compacting media
cites work: Solitary waves in magma dynamics
cites work: Generation and Creep of Magma in the Earth
cites work: Compressive solitary waves in compacting media
cites work: Q5835151
cites work: Q4275389
cites work: Q3331506
description: scientific article; zbMATH DE number 147210