Symmetric hyperbolic systems in algebras of generalized functions and distributional limits

Abstract

We study existence, uniqueness, and distributional aspects of generalized solutions to the Cauchy problem for first-order symmetric (or Hermitian) hyperbolic systems of partial differential equations with Colombeau generalized functions as coefficients and data. The proofs of solvability are based on refined energy estimates on lens-shaped regions with spacelike boundaries. We obtain several variants and also partial extensions of previous results and provide aspects accompanying related recent work by C. Garetto and M. Oberguggenberger.

References in corpus (3)

• Generalised hyperbolicity in conical space-times
• Generalised Fourier integral operator methods for hyperbolic equations with singularities
• The Cauchy problem for Schrödinger-type partial differential operators with generalized functions in the principal part and as data