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Generalized Fourier Integral Operator Methods for Hyperbolic Equations with Singularities
Published online by Cambridge University Press: 19 September 2013
Abstract
This paper addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalized functions. We employ the recently developed theory of generalized Fourier integral operators to construct parametrices for the solutions and to describe propagation of singularities in this setting. As required tools, the construction of generalized solutions to eikonal and transport equations is given and results on the microlocal regularity of the kernels of generalized Fourier integral operators are obtained.
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- Research Article
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- Copyright © Edinburgh Mathematical Society 2014
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