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.
Bertsch M.; Dal Passo R.; Nitsch C.
Oxford University Press
Interfaces and free boundaries (Print)