# On the Cauchy problem for the Fadaray tensor on globally hyperbolic manifolds with timelike boundary

June 12, 2023

We study the well-posedness of the Cauchy problem for the Faraday tensor on globally hyperbolic manifolds with timelike boundary. The existence of Green operators for the operator $\mathrm{d}+\delta$ and a suitable pre-symplectic structure on the space of solutions are discussed.

Keywords:

Overdetermined initial-boundary value problem, Maxwell’s equations, Faraday tensor, Cauchy problem, globally hyperbolic manifolds with timelike boundary.