COMPARISON OF SOME SOLUTION CONCEPTS FOR LINEAR FIRST-ORDER HYPERBOLIC DIFFERENTIAL EQUATIONS WITH NON-SMOOTH COEFFICIENTS

Abstract

We discuss solution concepts for linear hyperbolic equations with coefficients of regularity below Lipschitz continuity. Thereby our focus is on theories which are based either on a generalization of the method of charac- teristics or on refined techniques concerning energy estimates. We provide a series of examples both as simple illustrations of the notions and conditions involved but also to show logical independence among the concepts.