Comparison of some solution concepts for linear first-order hyperbolic differential equations with non-smooth coefficients

2007/12/11 by Haller, Simon, Hoermann, Guenther
#35D05 #35D10 #46F10 #46F30 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.0712.1669

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 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.

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