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

Irina Kmit

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

Analysis of PDEs 2025-12-10 v2

Authors: Irina Kmit

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

linear hyperbolic systems sobolev-type spaces periodic functions a priori estimates reflection boundary conditions

Cite

@article{arxiv.math/0702072,
  title  = {Hyperbolic Problems in the Whole Scale of Sobolev-Type Spaces of Periodic Functions},
  author = {Irina Kmit},
  journal= {arXiv preprint arXiv:math/0702072},
  year   = {2025}
}

Comments

15 pages. Section 5 is new

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