Symmetric hyperbolic systems in algebras of generalized functions and distributional limits

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 Hِrmann (2004) [26,23,16] and provide aspects accompanying related recent work in Oberguggenberger (2009), Garetto and Oberguggenberger (2011) [28,10,9].