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hyperbolic systems; periodic-Dirichlet problems; anisotropic Sobolev spaces; a priori estimates
We study one-dimensional linear hyperbolic systems with $L^{\infty}$-coeffici\-ents 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.
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