Weak entropy solutions for degenerate parabolic–hyperbolic inequalities Original Research Article

We study inner obstacle problems for a class of strongly degenerate parabolic–hyperbolic quasilinear operators associated with Dirichlet data in an open bounded subset of RpRp, p≥1p≥1. We first give the definition of a weak entropy solution that warrants uniqueness; the boundary conditions are expressed by using the framework of divergence measure fields. The existence of such a solution is obtained through the vanishing viscosity method.