Nonlinear Parabolic Equations with Spatial Discontinuities

Clément Cancès (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We consider a two phase flow involving no capillary barriers in a heterogeneous porous media, composed by an apposition of several homogeneous porous media. We prove the existence of a weak solution for such a flow using the convergence of a finite volume approximation. Then under the assumption that the equations governing the flows in each homogeneous porous media degenerate in not too different ways, we prove the uniqueness of the weak solution, using a doubling variable method. We also prove that such a solution belongs to C([0, T ], L p (Ω)) for any p ∈ [1, +∞).

Mots clés: porous media flow; spatial discontinuity; finite volume methods

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Clément Cancès. Nonlinear Parabolic Equations with Spatial Discontinuities. Nonlinear Differential Equations and Applications, 2008, 15, pp.427-456. ⟨hal-01713524⟩