Well-posedness of a class of infinite-dimensional port-Hamiltonian systems with boundary control and observation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915381068693504 |
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| author | Elghazi, Bouchra Jacob, Birgit Zwart, Hans |
| author_facet | Elghazi, Bouchra Jacob, Birgit Zwart, Hans |
| contents | We characterize the well-posedness of a class of infinite-dimensional port-Hamiltonian systems with boundary control and observation. This class includes in particular the Euler-Bernoulli beam equations and more generally 1D linear infinite-dimensional port-Hamiltonian systems with boundary control and observation as well as coupled systems. It is known, that for the Timoshenko beam models internal well-posedness implies well-posedness of the overall system. By means of an example we show that this is not true for the Euler-Bernoulli beam models. An easy verifiable equivalent condition for well-posedness of the overall system will be presented. We will conclude the paper by applying the obtained results to several Euler-Bernoulli beam models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_16862 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness of a class of infinite-dimensional port-Hamiltonian systems with boundary control and observation Elghazi, Bouchra Jacob, Birgit Zwart, Hans Analysis of PDEs Functional Analysis We characterize the well-posedness of a class of infinite-dimensional port-Hamiltonian systems with boundary control and observation. This class includes in particular the Euler-Bernoulli beam equations and more generally 1D linear infinite-dimensional port-Hamiltonian systems with boundary control and observation as well as coupled systems. It is known, that for the Timoshenko beam models internal well-posedness implies well-posedness of the overall system. By means of an example we show that this is not true for the Euler-Bernoulli beam models. An easy verifiable equivalent condition for well-posedness of the overall system will be presented. We will conclude the paper by applying the obtained results to several Euler-Bernoulli beam models. |
| title | Well-posedness of a class of infinite-dimensional port-Hamiltonian systems with boundary control and observation |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2501.16862 |