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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.21396 |
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| _version_ | 1866917094678855680 |
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| author | Ehrhardt, Matthias Glück, Jochen Petrov, Pavel Tappe, Stefan |
| author_facet | Ehrhardt, Matthias Glück, Jochen Petrov, Pavel Tappe, Stefan |
| contents | Pseudodifferential parabolic equations with an operator square root arise in wave propagation problems as a one-way counterpart of the Helmholtz equation. The expression under the square root usually involves a differential operator and a known function. We discuss a rigorous definition of such operator square roots and show well-posedness of the pseudodifferential parabolic equation by using the theory of strongly continuous semigroups. This provides a justification for a family of widely-used numerical methods for wavefield simulations in various areas of physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21396 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Square Root Operators and the Well-Posedness of Pseudodifferential Parabolic Models of Wave Phenomena Ehrhardt, Matthias Glück, Jochen Petrov, Pavel Tappe, Stefan Atmospheric and Oceanic Physics Analysis of PDEs Functional Analysis 35S10, 47G30, 76Q05 Pseudodifferential parabolic equations with an operator square root arise in wave propagation problems as a one-way counterpart of the Helmholtz equation. The expression under the square root usually involves a differential operator and a known function. We discuss a rigorous definition of such operator square roots and show well-posedness of the pseudodifferential parabolic equation by using the theory of strongly continuous semigroups. This provides a justification for a family of widely-used numerical methods for wavefield simulations in various areas of physics. |
| title | Square Root Operators and the Well-Posedness of Pseudodifferential Parabolic Models of Wave Phenomena |
| topic | Atmospheric and Oceanic Physics Analysis of PDEs Functional Analysis 35S10, 47G30, 76Q05 |
| url | https://arxiv.org/abs/2504.21396 |