A well-posedness result of a characteristic hyperbolic mixed problem

Abstract

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 $$L^{2}$$ well-posedness of the initial boundary value problem, provided that the source data of the interior is only $$L^{1}([0,T],L^{2}(\varOmega )),$$ with the aid of the paradifferential calculus.