Obstacle problems for a coupling of quasilinear hyperbolic-parabolic equations

Abstract

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 ${\Omega }_h$ with a quasilinear parabolic one set in the complementary ${\Omega }_p=\Omega \backslash {\Omega }_h$. The mathematical problem is motivated by physical models for infiltration processes with saturation thresholds.