Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws

We deal with the non characteristic initial and boundary value problem for an n × n strictly hyperbolic system of conservation laws in one space dimension ∂tu + ∂xF(u) = 0, u(0, x) = ū(x), b( u(ψ(t), t)) = g(t). (*) Here F is a smooth vector field defined in an open, convex neighborhood of the origin of ℝn, ū and g are functions with small total variation, x = ψ(t) is a non characteristic Lipschitz boundary profile, and b a C1function. We prove that the front tracking solutions to (*) constructed by D. Amadori in [1] are stable for the double-struck L sign1 topology. This implies the existence of a Standard Riemann Semigroup and hence the well-posedness of (*). © 2007 Birkhaueser.