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.
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Antonio Ros, Stable periodic constant mean curvature surfaces and mesoscopic phase separation. Interfaces Free Bound. 9 (2007), no. 3, pp. 355–365DOI 10.4171/IFB/168