A system of degenerate parabolic nonlinear PDE's: a new free boundary problem
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We prove existence of solutions of a new free boundary problem described by a system of degenerate parabolic equations. The problem arises in petroleum engineering and concerns fluid flows in diatomite rocks. The unknown functions represent the pressure of the fluid and a damage parameter of the porous rock. These quantities are not necessarily continuous on the free boundary, which considerably complicates the mathematical analysis.
oil engineering, nonlocal damage mechanics, Flows in porous media; filtration; seepage, nonlinear parabolic system, existence, Free boundary problems for PDEs, degenerate parabolic PDE's, petroleum engineering, Degenerate parabolic equations, Settore MAT/05 - ANALISI MATEMATICA, Geological problems
oil engineering, nonlocal damage mechanics, Flows in porous media; filtration; seepage, nonlinear parabolic system, existence, Free boundary problems for PDEs, degenerate parabolic PDE's, petroleum engineering, Degenerate parabolic equations, Settore MAT/05 - ANALISI MATEMATICA, Geological problems
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