Dissipative formulation of initial boundary value problems for Friedrichs’ systems

In this article we present a dissipative definition of a solution for initial boundary value problems for Friedrichs’ systems posed in the space . We study the information contained in this definition and prove an existence and uniqueness theorem in the non-characteristic case and with constant coefficients. Finally, we compare our choice of boundary condition to previous works, especially on the wave equation and show how to model additional constrained problems in view of initial boundary value problems for viscoplastic equations.