Comparison of Some Solution Concepts for Linear First-order Hyperbolic Differential Equations With Non-smooth Coefficients

Simon Haller, Gunther Hormann

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 characteristics 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.