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MICHIEL BERTSCH† Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico, 137, I-00161 Roma, Italy Dipartimento di Matematica, Universita degli Studi di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133 Roma, Italy ROBERTA DAL PASSO‡ AND CARLO NITSCH§ Dipartimento di Matematica, Universita degli Studi di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133 Roma, Italy

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