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Three-dimensional solutions of nonlinear degenerate diffusion-convection processes. (English) Zbl 0751.35020

This paper deals with a few properties of the solutions of a class of degenerate diffusion-convection equations. Under various boundary conditions an uniqueness result is proved in the three-dimensional case. Then the hyperbolic behavior of a free boundary is established. The method relies on a comparison principle. Finally existence and behavior of a break-through time are investigated when dealing with the motion of two immiscible incompressible fluids.

MSC:

35K57 Reaction-diffusion equations
35K65 Degenerate parabolic equations
76S05 Flows in porous media; filtration; seepage
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35Q35 PDEs in connection with fluid mechanics
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