Geodesic
A system of degenerate parabolic nonlinear PDE's: a new free boundary problem
Michiel Bertsch1 ; Roberta Dal Passo2 ; Carlo Nitsch3
1Consiglio Nazionale delle Ricerche, Roma, Italy
2Università di Roma, Italy
3Università degli Studi di Napoli Federico II, Italy
Interfaces and free boundaries, Tome 7 (2005) no. 3, pp. 255-276

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DOI

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.
DOI : 10.4171/ifb/124
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Nonlinear parabolic system, degenerate parabolic PDE's, nonlocal damage mechanics, oil engineering

Michiel Bertsch  1   ; Roberta Dal Passo  2   ; Carlo Nitsch  3

1 Consiglio Nazionale delle Ricerche, Roma, Italy
2 Università di Roma, Italy
3 Università degli Studi di Napoli Federico II, Italy 
Michiel Bertsch; Roberta Dal Passo; Carlo Nitsch. A system of degenerate parabolic nonlinear PDE's: a new free boundary problem. Interfaces and free boundaries, Tome 7 (2005) no. 3, pp. 255-276. doi: 10.4171/ifb/124
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     title = {A system of degenerate parabolic nonlinear {PDE's:} a new free boundary problem},
     journal = {Interfaces and free boundaries},
     pages = {255--276},
     year = {2005},
     volume = {7},
     number = {3},
     doi = {10.4171/ifb/124},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/124/}
}
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