Symmetric hyperbolic systems in algebras of generalized functions and distributional limits

摘要

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 in Oberguggenberger (1989), Lafon and Oberguggenberger (1991), and Hörmann (2004) and provide aspects accompanying related recent work in Oberguggenberger (2009), Garetto and Oberguggenberger (2011) .