Strong boundary traces and well-posedness for scalar conservation laws with dissipative boundary conditions
Résumé
The aim of this paper is to give sense to the following formal problem for a scalar conservation law with boundary condition (BC, in the sequel) : u_t + div \phi(u) = f in Q := (0, T) ×\Omega u(0, ·) = u_0 on \Omega \phi_v(u) := \phi(u) ·v ∈ \beta(u) on \Sigma := (0, T) × \partial\Omega. Here v is the unit outward normal vector on \partial\Omega, the function\phi : R → R^N is continuous, and \beta is a maximal monotone graph on R.