Continuous Data Assimilation for Semilinear Parabolic Equations: A General Approach by Evolution Equations
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911464869068800 |
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| author | Del Sarto, Gianmarco Hieber, Matthias Palma, Filippo Zöchling, Tarek |
| author_facet | Del Sarto, Gianmarco Hieber, Matthias Palma, Filippo Zöchling, Tarek |
| contents | This article develops a general framework for continuous deterministic data assimilation for semilinear parabolic equations by means of evolution equations. Introducing a nudged model driven by partial observations, the global well-posedness of the reference and the approximating systems is established under natural assumptions. In addition, it is shown that the approximating solution converges exponentially to the solution of the reference system, provided the observational resolution and the nudging parameter are suitably chosen. The approach allows us to consider many systems, such as the Allen-Cahn, Cahn-Hilliard, Sellers-type energy balance, and bidomain systems, for the first time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20769 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Continuous Data Assimilation for Semilinear Parabolic Equations: A General Approach by Evolution Equations Del Sarto, Gianmarco Hieber, Matthias Palma, Filippo Zöchling, Tarek Analysis of PDEs Mathematical Physics 35K90, 35K55, 47D06, 47J35, 35B40, 76U60 This article develops a general framework for continuous deterministic data assimilation for semilinear parabolic equations by means of evolution equations. Introducing a nudged model driven by partial observations, the global well-posedness of the reference and the approximating systems is established under natural assumptions. In addition, it is shown that the approximating solution converges exponentially to the solution of the reference system, provided the observational resolution and the nudging parameter are suitably chosen. The approach allows us to consider many systems, such as the Allen-Cahn, Cahn-Hilliard, Sellers-type energy balance, and bidomain systems, for the first time. |
| title | Continuous Data Assimilation for Semilinear Parabolic Equations: A General Approach by Evolution Equations |
| topic | Analysis of PDEs Mathematical Physics 35K90, 35K55, 47D06, 47J35, 35B40, 76U60 |
| url | https://arxiv.org/abs/2602.20769 |