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.
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Roberta Dal Passo, Michiel Bertsch, Carlo Nitsch, A system of degenerate parabolic nonlinear PDE's: a new free boundary problem. Interfaces Free Bound. 7 (2005), no. 3, pp. 255–276DOI 10.4171/IFB/124