JournalsifbVol. 10, No. 3pp. 377–398

Traveling wave solutions of a nonlinear degenerate parabolic system from petroleum engineering

  • Michiel Bertsch

    Consiglio Nazionale delle Ricerche, Roma, Italy
  • Carlo Nitsch

    Università degli Studi di Napoli Federico II, Italy
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Abstract

We study existence and qualitative properties of traveling wave solutions of a new free boundary problem which describes fluid flow in diatomite rocks. Diatomites are rather fragile and are characterized by a low permeability, which can increase due to the nonlocal accumulation of damage caused by the fluid flow. The traveling wave solutions give insight in the behavior near the free boundaries and show a strong parameter dependence. In particular we find in certain parameter ranges solutions with discontinuities across the free boundaries.

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Michiel Bertsch, Carlo Nitsch, Traveling wave solutions of a nonlinear degenerate parabolic system from petroleum engineering. Interfaces Free Bound. 10 (2008), no. 3, pp. 377–398

DOI 10.4171/IFB/194