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

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.

15 pages. Section 5 is new

References in corpus (1)

• Fredholm Alternative for Periodic-Dirichlet Problems for Linear Hyperbolic Systems

Cited by in corpus (1)

• Fredholmness and Smooth Dependence for Linear Time-Periodic Hyperbolic System