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

TL;DR

This paper investigates how singularities propagate in solutions to wave equations with discontinuous coefficients using Colombeau algebras, providing bounds on singular support and establishing new existence results under weaker assumptions.

Contribution

It introduces new existence results for generalized solutions with weaker assumptions and analyzes singularity propagation in wave equations with discontinuous coefficients.

Findings

Bounds on singular support of solutions

Existence results under weaker assumptions

Applicability to various wave equations and systems

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.