Christian Spreitzer (University of Vienna)
Hyperbolic first-order systems with non-smooth coefficients
Abstract:
The Dirac equation provides a relativistic description of spin-1/2 particles. Non-smooth interaction terms in this equation lead to first order PDE-systems with distributional coefficients. Colombeau's theory of generalized functions allows to handle such equations on a mathematically sound basis. I will present an existence and uniqueness result for symmetric hyperbolic first-order PDE-systems in the special Colombeau algebra. I will also give a sketch of the proof and discuss some future work in the same direction.
This is work in collaboration with Günther Hörmann.
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