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On the existence of compressive solitary waves in compacting media. (English) Zbl 0841.76087

Summary: Necessary conditions for the existence of compressive solitary-wave solutions which describe the two-phase fluid flow in a medium compacting under gravity are derived. It is shown that for the existence of compressive solitary-wave solutions which satisfy certain boundary conditions it is necessary that \(n= m>1\) where \(n\) and \(m\) are the exponents in power laws relating the permeability of the medium and the viscosity of the solid matrix, respectively, to the voidage. The effect of the value of the exponents \(n\) and \(m\) on the shape of the solitary wave is investigated by using existing analytical solutions and new numerical solutions.

MSC:

76T99 Multiphase and multicomponent flows
35Q51 Soliton equations
86A60 Geological problems
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