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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.16232 |
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| _version_ | 1866912341620162560 |
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| author | Panov, Evgeny Yu. |
| author_facet | Panov, Evgeny Yu. |
| contents | We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest a criteria of uniqueness of this semigroup. We also find a stronger criteria of uniqueness of generalized solutions. Applications to transport equations with solenoidal (and generally discontinuous) coefficients are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16232 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On evolutionary equations related to skew-symmetric spatial operators Panov, Evgeny Yu. Analysis of PDEs We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest a criteria of uniqueness of this semigroup. We also find a stronger criteria of uniqueness of generalized solutions. Applications to transport equations with solenoidal (and generally discontinuous) coefficients are given. |
| title | On evolutionary equations related to skew-symmetric spatial operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.16232 |