Exponential Dichotomy for Hyperbolic Systems with Periodic Boundary Conditions

TL;DR

This paper establishes explicit conditions under which linear hyperbolic systems with periodic boundary conditions exhibit exponential dichotomies, advancing the understanding of their stability and spectral properties.

Contribution

It provides explicit criteria for the existence of exponential dichotomies in hyperbolic systems with periodic boundary conditions, a novel contribution to the stability analysis of such systems.

Findings

Derived explicit conditions for exponential dichotomies

Applied results to hyperbolic systems with periodic boundary conditions

Enhanced understanding of stability in hyperbolic PDEs

Abstract

We investigate evolution families generated by general linear first-order hyperbolic systems in one space dimension with periodic boundary conditions. We state explicit conditions on the coefficient functions that are sufficient for the existence of exponential dichotomies on $\R$ in the space of continuous periodic functions.