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Generation and creep of magma in the earth. (English) Zbl 0665.76110
This paper describes a model representing the process of partial melting of deforming mantle rock, and the associated melt migration due to differential buoyancy. The model is a double free-boundary problem of degenerate type, and is typical of such slow, reactive two-phase flows. Prescription of boundary conditions is problematical, but in some sense the model picks its own; a realistic asymptotic solution involving rather novel boundary layer behaviour is presented, for the case of two fixed boundaries, and it is then shown how the free boundaries can be determined a posteriori. The implications for geophysical behaviour are discussed.

MSC:
76R99 Diffusion and convection
76T99 Multiphase and multicomponent flows
86A99 Geophysics
35B25 Singular perturbations in context of PDEs
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