A well-posedness result of a characteristic hyperbolic mixed problem

We study the well-posedness of a hyperbolic characteristic initial boundary value problem with Lipschitz continuous coefficients. Assuming more general boundary assumptions than those of maximally dissipativeness, we deal with a Friedrichs symmetrizable system of first order satisfying a minimal structure boundary condition, the so-called Uniform Kreiss-Lopatinskii Condition. We show that a semi-group estimate holds, leading to the proof of the L2 well-posedness of the initial boundary value problem, provided that the source data of the interior is only L1([0,T],L2(Omega)), with the aid of the paradifferential calculus.