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arXiv · 2510.10571

Determining nonlinear balance laws in product-type domains by a single local passive boundary observation

Chaohua Duan·Hongyu Liu·Qingle Meng·Li Wang
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Abstract

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.

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Chaohua Duan, Hongyu Liu, Qingle Meng, Li Wang. 2025-10-12. Determining nonlinear balance laws in product-type domains by a single local passive boundary observation. https://arxiv.org/abs/2510.10571

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