Perturbations of superstable linear hyperbolic systems

Abstract

The paper deals with initial-boundary value problems for linear non-autonomous first order hyperbolic systems whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in $L^2$ as well as in $C^1$ under small bounded perturbations. To show this for $C^1$, we prove a general smoothing result implying that the solutions to the perturbed problems become eventually $C^1$-smooth for any $L^2$-initial data.

arXiv comment29 pages, final version

References in corpus (3)

• Classical solvability of nonlinear initial-boundary problems for first-order hyperbolic systems
• Smoothing Solutions to Initial-Boundary Problems for First-Order Hyperbolic Systems
• Smoothing effect and Fredholm property for first-order hyperbolic PDEs

Cited by in corpus (6)

• Classical Bounded and Almost Periodic Solutions to Quasilinear First-Order Hyperbolic Systems in a Strip
• On the bounded smooth solutions to exponentially stable linear nonautonomous hyperbolic systems
• Lyapunov function and smooth periodic solutions to quasilinear 1D hyperbolic systems
• 1D Hyperbolic Systems with Nonlinear Boundary Conditions II: Criteria for Finite Time Stability
• Finite Time Stabilization of Nonautonomous First Order Hyperbolic Systems
• Exponential stability of solutions to perturbed superstable wave equations