Stability via closure relations with applications to dissipative and port-Hamiltonian systems

2022/12/22 by Jochen Glück, Glück, Jochen, Birgit Jacob +7
Computer Science · Engineering · #34G10 #37K40 #47D06 #93D23 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Dynamics and Pattern Formation #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2212.12025

openalex publication_date 2022/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider differential operators A that can be represented by means of a so-called closure relation in terms of a simpler operator A_ext defined on a larger space. We analyze how the spectral properties of A and A_ext are related and give sufficient conditions for exponential stability of the semigroup generated by A in terms of the semigroup generated by A_ext. As applications we study the long-term behaviour of a coupled wave-heat system on an interval, parabolic equations on bounded domains that are coupled by matrix valued potentials, and of linear infinite-dimensional port-Hamiltonian systems with dissipation on an interval.

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