A Semigroup Approach to W1,∞-Solutions to a Class of Quasilinear Hyperbolic Systems

In this paper we present a local existence and uniqueness theorem for a W1,∞-solution to a quasilinear first order system based on semigroup theory. We apply abstract theorems on nonautonomous linear evolution equations to the linearized system and solve the quasilinear system by a fixed point argument.