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We consider the Dirac operator on globally hyperbolic manifolds with timelikeboundary and show well-posedness of the Cauchy initial-boundary value problemcoupled to MIT-boundary conditions. This is achieved by transforming theproblem locally into a symmetric positive hyperbolic system, proving existenceand uniqueness of weak solutions and then using local methods developed by Lax,Phillips and Rauch, Massey to show smoothness of the solutions. Our proofactually works for a slightly more general class of local boundary conditions.

The well-posedness of the Cauchy problem for the Dirac operator on globally hyperbolic manifolds with timelike boundary