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.
A system of degenerate parabolic nonlinear PDE's: a new free boundary problem / M., Bertsch; R., Dal Passo; Nitsch, Carlo. - In: INTERFACES AND FREE BOUNDARIES. - ISSN 1463-9963. - STAMPA. - 7:(2005), pp. 255-276.
A system of degenerate parabolic nonlinear PDE's: a new free boundary problem
NITSCH, CARLO
2005
Abstract
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.| File | Dimensione | Formato | |
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