Analysis of coupled Maxwell-cable problems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912666354712576 |
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| author | Reis, Timo Skrepek, Nathanael |
| author_facet | Reis, Timo Skrepek, Nathanael |
| contents | Building on the recently published work "Modeling of radiating curved cables via coupled telegrapher's and Maxwell's equations", which introduces a model for the interaction between electromagnetic fields and radiating (possibly curved) cables, we analyze the qualitative properties of the resulting dynamical system. The model features inputs and outputs given by the currents and voltages at the cable ends, while the state comprises the corresponding distributions along the cables and the electromagnetic fields in the surrounding domain. We show that the autonomous dynamics (i.e., with zero input) generate a strongly continuous semigroup and establish sufficient conditions for well-posedness, meaning continuous dependence of the state and output trajectories on the inputs and initial conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20619 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of coupled Maxwell-cable problems Reis, Timo Skrepek, Nathanael Analysis of PDEs Functional Analysis 35Q61, 37L05, 78A25, 93B28, 93C25 Building on the recently published work "Modeling of radiating curved cables via coupled telegrapher's and Maxwell's equations", which introduces a model for the interaction between electromagnetic fields and radiating (possibly curved) cables, we analyze the qualitative properties of the resulting dynamical system. The model features inputs and outputs given by the currents and voltages at the cable ends, while the state comprises the corresponding distributions along the cables and the electromagnetic fields in the surrounding domain. We show that the autonomous dynamics (i.e., with zero input) generate a strongly continuous semigroup and establish sufficient conditions for well-posedness, meaning continuous dependence of the state and output trajectories on the inputs and initial conditions. |
| title | Analysis of coupled Maxwell-cable problems |
| topic | Analysis of PDEs Functional Analysis 35Q61, 37L05, 78A25, 93B28, 93C25 |
| url | https://arxiv.org/abs/2510.20619 |