Hideo Deguchi, Michael Oberguggenberger
Published 2015-07-30Version 1
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.
Partial continuity for nonlinear systems with nonstandard growth and discontinuous coefficients
Stability for solutions of wave equations with C^{1,1} coefficients
The wave equation with a discontinuous coefficient depending on time only: generalized solutions and propagation of singularities
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