A Bilateral Obstacle Problem for a Class of Degenerate Parabolic-Hyperbolic Operators.

Laurent Levi (1) , Guy Vallet (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

We investigate some inner bilateral obstacle problems for a class of strongly degenerate parabolic-hyperbolic quasilinear operators associated with homogeneous Dirichlet data in a multidimensional bounded domain. We first introduce the concept of an entropy process solution, more convenient and generalizing the notion of an entropy solution. Moreover, the boundary conditions are expressed by using the background of Divergence Measure Fields. We ensure that proposed definition warrants uniqueness. The existence of an entropy process solution is obtained through the vanishing viscosity and penalization methods.

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Levi, Guy Vallet. A Bilateral Obstacle Problem for a Class of Degenerate Parabolic-Hyperbolic Operators.. 2006. ⟨hal-00220963⟩