Abstract:We study one-dimensional linear hyperbolic systems with $L^{\infty }$-coefficients subjected to periodic conditions in time and reflection boundary conditions in space. We derive a priori estimates and give an operator representation of solutions in the whole scale of Sobolev-type spaces of periodic functions. These spaces give an optimal regularity trade-off for our problem.
Keywords: hyperbolic systems, periodic-Dirichlet problems, anisotropic Sobolev spaces, a priori estimates
AMS Subject Classification: 35L50