Block operator matrix techniques for stability properties of hyperbolic equations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914387796688896 |
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| author | Waurick, Marcus |
| author_facet | Waurick, Marcus |
| contents | Inspired by recent developments in the theory of stability results in the context of certain wave type phenomena, we discuss abstract damped hyperbolic type equations given in a block operator matrix form with regards to asymptotic behaviour of their solutions. Under mild conditions on the operators involved we provide criteria establishing strong or semi-uniform stability. In the particular case of Maxwell's equations, these criteria are implied under mild regularity conditions of the underlying domain causing spatial derivative operators satisfy certain compact embedding conditions and rather minimal assumptions on the damping conductivity. These assumptions improve on both regularity as well as on the structural requirements for the conductivity previously available in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12005 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Block operator matrix techniques for stability properties of hyperbolic equations Waurick, Marcus Analysis of PDEs Functional Analysis 35B40, 35Q61, 47A53, 47A05, 47A62 Inspired by recent developments in the theory of stability results in the context of certain wave type phenomena, we discuss abstract damped hyperbolic type equations given in a block operator matrix form with regards to asymptotic behaviour of their solutions. Under mild conditions on the operators involved we provide criteria establishing strong or semi-uniform stability. In the particular case of Maxwell's equations, these criteria are implied under mild regularity conditions of the underlying domain causing spatial derivative operators satisfy certain compact embedding conditions and rather minimal assumptions on the damping conductivity. These assumptions improve on both regularity as well as on the structural requirements for the conductivity previously available in the literature. |
| title | Block operator matrix techniques for stability properties of hyperbolic equations |
| topic | Analysis of PDEs Functional Analysis 35B40, 35Q61, 47A53, 47A05, 47A62 |
| url | https://arxiv.org/abs/2603.12005 |