1D Hyperbolic Systems with Nonlinear Boundary Conditions II: Criteria for Finite Time Stability

TL;DR

This paper establishes criteria for finite time stability of 1D hyperbolic systems with nonlinear boundary conditions, providing necessary and sufficient conditions based on propagation operators along characteristics.

Contribution

It introduces new criteria for finite time stability of hyperbolic systems with nonlinear boundaries, extending previous results to more general conditions.

Findings

Criteria for finite time stability are derived.

Conditions are expressed via propagation operators along characteristics.

Results apply to both continuous and $L^2$-generalized solutions.

Abstract

We investigate the finite time stability property of one-dimensional nonautonomous initial boundary value problems for linear decoupled hyperbolic systems with nonlinear boundary conditions. We establish sufficient and necessary conditions under which continuous or $L^2$-generalized solutions stabilize to zero in a finite time. Our criteria are expressed in terms of a propagation operator along characteristic curves.