Scalar Conservation Laws with Discontinuous Flux in Several Space Dimensions

J. Jimenez (1)

1 LMAP - Laboratoire de Mathématiques appliquées de Pau

We deal with a scalar conservation law, set in a bounded multidimensional domain, and such that the convective term is discontinuous with respect to the space variable. We introduce a weak entropy formulation for the homogeneous Dirichlet problem associated with the first-order reaction-diffusion equation that we consider. We establish an existence and uniqueness property for the weak entropy solution. The method of doubling variables is used to state uniqueness while the vanishing viscosity method allows us to prove the existence result.

Domaines: Equations aux dérivées partielles [math.AP]

J. Jimenez. Scalar Conservation Laws with Discontinuous Flux in Several Space Dimensions. 2008. ⟨hal-00267446⟩