Theory And Applications Of One-Sided Coupled Operator Matrices
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908684068585472 |
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| author | Kramar, Marjeta Mugnolo, Delio Nagel, Rainer |
| author_facet | Kramar, Marjeta Mugnolo, Delio Nagel, Rainer |
| contents | The theory of one-sided coupled operator matrices, recently introduced by K.-J. Engel, is an abstract framework for concrete initial value problems and allows complete information on well-posedness, and stability of solutions. These notes are meant as a survey on this rich theory, with a particular stress on applications to initial-boundary value problems with unbounded boundary feedbacks. A diffusion-transport system with dynamical boundary conditions is discussed, and its well-posedness and various other properties are investigated. As a by-product, the well-posedness of a wave equation with dynamical boundary condition is also obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01719 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Theory And Applications Of One-Sided Coupled Operator Matrices Kramar, Marjeta Mugnolo, Delio Nagel, Rainer Analysis of PDEs Primary 47D06, Secondary 35K99, 47B65 The theory of one-sided coupled operator matrices, recently introduced by K.-J. Engel, is an abstract framework for concrete initial value problems and allows complete information on well-posedness, and stability of solutions. These notes are meant as a survey on this rich theory, with a particular stress on applications to initial-boundary value problems with unbounded boundary feedbacks. A diffusion-transport system with dynamical boundary conditions is discussed, and its well-posedness and various other properties are investigated. As a by-product, the well-posedness of a wave equation with dynamical boundary condition is also obtained. |
| title | Theory And Applications Of One-Sided Coupled Operator Matrices |
| topic | Analysis of PDEs Primary 47D06, Secondary 35K99, 47B65 |
| url | https://arxiv.org/abs/2512.01719 |