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Nonisothermal two-phase filtration in porous media. (English) Zbl 0818.35087

Antontsev, S. N. (ed.) et al., Free boundary problems in continuum mechanics. International conference on free boundary problems in continuum mechanics, Novosibirsk, Russia, July 15-19, 1991. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 106, 121-130 (1992).
Summary: The paper deals with a mathematical model (MLT model) which takes into account the effect of heat processes on fluid motion character via the change of viscosity and capillary properties of different inhomogeneous fluid components depending on their temperature and that of porous medium.
The peculiarity of the MLT model is that all the components of its equation, except the Darcy and Laplace laws, are a consequence of the conservation laws in continuum mechanics. In particular, the motion of contact boundaries of inhomogeneous fluid with its immovable components (the Stefan type problem) are described within the framework of this model.
The aim of this paper is to determine the dependence of smoothness of the solutions to the initial boundary value problems for the MLT model (MLT problems) on the coefficients of equations and boundary conditions. The results obtained are applied then to prove convergence of the iterative method for solving the MLT problem and to find the velocity of this convergence.
For the entire collection see [Zbl 0807.00016].

MSC:

35Q35 PDEs in connection with fluid mechanics
76S05 Flows in porous media; filtration; seepage
76T99 Multiphase and multicomponent flows
80A20 Heat and mass transfer, heat flow (MSC2010)
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