A system of degenerate parabolic nonlinear PDE's: a new free boundary problem
Roberta Dal Passo
Università di Roma, ItalyMichiel Bertsch
Consiglio Nazionale delle Ricerche, Roma, ItalyCarlo Nitsch
Università degli Studi di Napoli Federico II, Italy
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.
Cite this article
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. 255–276
DOI 10.4171/IFB/124