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Hyperbolic Problems in the Whole Scale of Sobolev-Type Spaces of Periodic Functions

Irina Kmit
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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.

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Irina Kmit. 2007-02-04. Hyperbolic Problems in the Whole Scale of Sobolev-Type Spaces of Periodic Functions. https://arxiv.org/abs/math/0702072

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