Robustness of Exponential Dichotomies of Boundary-Value Problems for General First-Order Hyperbolic Systems

TL;DR

This paper investigates the stability of exponential dichotomies in boundary value problems for first-order hyperbolic systems, demonstrating their persistence under small coefficient perturbations in the space of continuous functions.

Contribution

It establishes the robustness of exponential dichotomies for hyperbolic systems with smoothing boundary conditions under small perturbations.

Findings

Exponential dichotomies are stable under small coefficient changes.

Boundary conditions like reflection preserve smoothing solutions.

Robustness holds in the space of continuous functions.

Abstract

We examine robustness of exponential dichotomies of boundary value problems for general linear first-order one-dimensional hyperbolic systems. The boundary conditions are supposed to be of types ensuring smoothing solutions in finite time, which includes reflection boundary conditions. We show that the dichotomy survives in the space of continuous functions under small perturbations of all coefficients in the differential equations.