JournalsifbVol. 7 , No. 3DOI 10.4171/ifb/124

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

  • Roberta Dal Passo

    Università di Roma, Italy
  • Michiel Bertsch

    Consiglio Nazionale delle Ricerche, 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

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.