We establish the existence and uniqueness of the solution to some inner obstacle problems for a coupling of a multidimensional quasilinear first-order hyperbolic equation set in a region with a quasilinear parabolic one set in the complementary . The mathematical problem is motivated by physical models for infiltration processes with saturation thresholds.
Cite this article
Laurent Lévi, Obstacle problems for a coupling of quasilinear hyperbolic-parabolic equations. Interfaces Free Bound. 9 (2007), no. 3, pp. 331–354DOI 10.4171/IFB/167