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

Jochen Glück; Birgit Jacob; Annika Meyer; Christian Wyss; Hans Zwart

doi:10.1007/s00028-024-00992-5

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

Jochen Glück^*, Birgit Jacob, Annika Meyer, Christian Wyss, Hans Zwart

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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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 analyse 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.

Original language	English
Article number	62
Journal	Journal of evolution equations
Volume	24
Issue number	3
Early online date	5 Jul 2024
DOIs	https://doi.org/10.1007/s00028-024-00992-5
Publication status	Published - Sept 2024

Keywords

34G10
37K40
47D06
93D23
C-semigroups
Closure relations
Exponential stability
Port-Hamiltonian systems

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10.1007/s00028-024-00992-5Licence: CC BY

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title = "Stability via closure relations with applications to dissipative and port-Hamiltonian systems",

abstract = "We consider differential operators A that can be represented by means of a so-called closure relation in terms of a simpler operator Aext defined on a larger space. We analyse how the spectral properties of A and Aext are related and give sufficient conditions for exponential stability of the semigroup generated by A in terms of the semigroup generated by Aext. 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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T1 - Stability via closure relations with applications to dissipative and port-Hamiltonian systems

AU - Glück, Jochen

AU - Jacob, Birgit

AU - Meyer, Annika

AU - Wyss, Christian

AU - Zwart, Hans

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/9

Y1 - 2024/9

N2 - We consider differential operators A that can be represented by means of a so-called closure relation in terms of a simpler operator Aext defined on a larger space. We analyse how the spectral properties of A and Aext are related and give sufficient conditions for exponential stability of the semigroup generated by A in terms of the semigroup generated by Aext. 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.

AB - We consider differential operators A that can be represented by means of a so-called closure relation in terms of a simpler operator Aext defined on a larger space. We analyse how the spectral properties of A and Aext are related and give sufficient conditions for exponential stability of the semigroup generated by A in terms of the semigroup generated by Aext. 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.

KW - 34G10

KW - 37K40

KW - 47D06

KW - 93D23

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KW - Closure relations

KW - Exponential stability

KW - Port-Hamiltonian systems

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DO - 10.1007/s00028-024-00992-5

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VL - 24

JO - Journal of evolution equations

JF - Journal of evolution equations

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M1 - 62

ER -

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

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