Hyperbolic Problems in the Whole Scale of Sobolev-Type Spaces of Periodic Functions
Abstract
We study one-dimensional linear hyperbolic systems with L∞-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.
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