Propagation of singularities for generalized solutions to wave equations with discontinuous coefficients

2015/07/30 by Hideo Deguchi, Deguchi, Hideo, Michael Oberguggenberger +1
Arts and Humanities · Mathematics · #35A21 #35B65 #35L05 #35L45 #46F30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Analysis #Philosophy and History of Science

paper · pdf · doi:10.48550/arxiv.1507.08465

openalex publication_date 2015/07/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

This article addresses linear hyperbolic partial differential equations with non-smooth coefficients and distributional data. Solutions are studied in the framework of Colombeau algebras of generalized functions. Its aim is to prove upper and lower bounds for the singular support of generalized solutions for wave equations with discontinuous coefficients. New existence results with weaker assumptions on the representing families are required and proven. The program is carried through for various types of one- and multidimensional wave equations and hyperbolic systems.

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