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

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

2007-02-04

arxiv.org/abs/math/0702072v2

Mathematics

Analysis of PDEs

15 pages. Section 5 is new

Scientific paper

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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