2025/11/28 by Roschkowski, Marco, Gernandt, Hannes
Engineering · Physics and Astronomy · #Analysis of PDEs (math.AP) #Control and Stability of Dynamical Systems #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations
paper · doi:10.48550/arxiv.2511.23336
openalex publication_date 2025/11/28 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28
We develop two local energy methods for distributed parameter port-Hamiltonian (pH) systems on one-dimensional spatial domains. The methods are applied to derive a characterization of exponential stability directly in terms of the energy passing through the boundary over a given time horizon. The resulting condition is verified for a network of vibrating strings where existing sufficient conditions cannot be applied. Moreover, we use a local energy method to study the short-time behavior of pH systems with boundary damping which was recently studied in the context of hypocoercivity.