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

2007/02/04 by Irina Kmit, Kmit, Irina
Engineering · Mathematics · #35L50 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.math/0702072

openalex publication_date 2007/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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