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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.10571 |
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| _version_ | 1866909840029253632 |
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| author | Duan, Chaohua Liu, Hongyu Meng, Qingle Wang, Li |
| author_facet | Duan, Chaohua Liu, Hongyu Meng, Qingle Wang, Li |
| contents | This paper introduces an operator-theoretic paradigm for solving inverse problems in nonlinear balance laws, shifting the focus from identifying specific functional forms to recovering the input-output actions of the associated flux and source operators. It is established that a single local passive boundary observation suffices to uniquely determine realizations of these operators for systems posed on product-type domains. This framework, which encompasses dynamical regimes, reveals a holographic-type principle where macroscopic boundary data encodes microscopic dynamical information, with broad implications for fluid dynamics and reaction-diffusion systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10571 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Determining nonlinear balance laws in product-type domains by a single local passive boundary observation Duan, Chaohua Liu, Hongyu Meng, Qingle Wang, Li Analysis of PDEs Mathematical Physics 35R30, 35R35, 47H30 This paper introduces an operator-theoretic paradigm for solving inverse problems in nonlinear balance laws, shifting the focus from identifying specific functional forms to recovering the input-output actions of the associated flux and source operators. It is established that a single local passive boundary observation suffices to uniquely determine realizations of these operators for systems posed on product-type domains. This framework, which encompasses dynamical regimes, reveals a holographic-type principle where macroscopic boundary data encodes microscopic dynamical information, with broad implications for fluid dynamics and reaction-diffusion systems. |
| title | Determining nonlinear balance laws in product-type domains by a single local passive boundary observation |
| topic | Analysis of PDEs Mathematical Physics 35R30, 35R35, 47H30 |
| url | https://arxiv.org/abs/2510.10571 |