JournalsifbVol. 7, No. 3pp. 255–276

A system of degenerate parabolic nonlinear PDE's: a new free boundary problem

  • Michiel Bertsch

    Consiglio Nazionale delle Ricerche, Roma, Italy

  • Roberta Dal Passo

    Università di Roma, Italy

  • Carlo Nitsch

    Università degli Studi di Napoli Federico II, Italy
A system of degenerate parabolic nonlinear PDE's: a new free boundary problem cover
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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

Michiel Bertsch, Roberta Dal Passo, 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