Fluid flow in a layered medium. (English) Zbl 0815.35038

A fluid flow through a fractured reservoir is modelled as the flow through relatively flat cells within a spatial region. An expression is derived for the exchange of fluid between the individual cells and the fissure system, which accounts for the secondary effects of both storage and flux. This gives a quasilinear parabolic system of partial differential equations coupled by the exchange term and the boundary values. Using a variational setting of the problem, the authors establish the existence and uniqueness of the solution and present some results on the continuous dependence of the solution on boundary conditions.
Reviewer: O.Titow (Berlin)


35K55 Nonlinear parabolic equations
35K65 Degenerate parabolic equations
35Q35 PDEs in connection with fluid mechanics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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