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

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.

18 pages

References in corpus (1)

• Smoothing effect and Fredholm property for first-order hyperbolic PDEs

Cited by in corpus (3)

• Classical Bounded and Almost Periodic Solutions to Quasilinear First-Order Hyperbolic Systems in a Strip
• Exponential Dichotomy for Hyperbolic Systems with Periodic Boundary Conditions
• Lyapunov function and smooth periodic solutions to quasilinear 1D hyperbolic systems