Propagation of Singularities for Generalized Solutions to Wave Equations with Discontinuous Coefficients

Hideo Deguchi, Michael Oberguggenberger

Type: Article

Publication Date: 2016-01-01

Citations: 11

DOI: https://doi.org/10.1137/15m1032661

Abstract

This article addresses linear hyperbolic partial differential equations with nonsmooth 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 proved. The program is carried through for various types of one- and multidimensional wave equations and hyperbolic systems.

Locations

arXiv (Cornell University) - View - PDF
SIAM Journal on Mathematical Analysis - View

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Works Cited by This (37)

Action	Title	Year	Authors
+	None	2001	Günther Hörmann Maarten V. de Hoop
+	Multiplication of Distributions and Applications to Partial Differential Equations	1992	Michael Oberguggenberger
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+	Elementary Introduction to New Generalized Functions	1985	J. F. Colombeau
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+	Microlocal hypoellipticity of linear partial differential operators with generalized functions as coefficients	2005	Günther Hörmann Michael Oberguggenberger Stevan Pilipović
+	Hyperbolic systems with discontinuous coefficients: Generalized solutions and a transmission problem in acoustics	1989	Michael Oberguggenberger
+ PDF Chat	Hyperbolic operators with non-Lipschitz coefficients	1995	Ferruccio Colombini Nicolás Lerner