Observability for heat equations with time-dependent analytic memory
Wang G, Zhang Y, Zuazua Iriondo E (2024)
Publication Language: English
Publication Status: Submitted
Publication Type: Journal article
Future Publication Type: Journal article
Publication year: 2024
Journal
Book Volume: 248
Journal Issue: 115
DOI: 10.1007/s00205-024-02058-9
Abstract
This paper presents a complete analysis of the observability property of heat equations with time-dependent real analytic memory kernels. More precisely, we characterize the geometry of the space-time measurable observation sets ensuring sharp observability inequalities, which are relevant both for control and inverse problems purposes. Despite the abundant literature on the observation of heat-like equations, existing methods do not apply to models involving memory terms. We present a new methodology and observation strategy, relying on the decomposition of the flow, the time-analyticity of solutions and the propagation of singularities. This allows us to obtain a sufficient and necessary geometric condition on the measurable observation sets for sharp two-sided observability inequalities. In addition, some applications to control and relevant open problems are presented.
Authors with CRIS profile
Yubiao Zhang
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Enrique Zuazua Iriondo
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
China (CN)How to cite
APA:
Wang, G., Zhang, Y., & Zuazua Iriondo, E. (2024). Observability for heat equations with time-dependent analytic memory. Archive for Rational Mechanics and Analysis, 248(115). https://doi.org/10.1007/s00205-024-02058-9
MLA:
Wang, Gengsheng, Yubiao Zhang, and Enrique Zuazua Iriondo. "Observability for heat equations with time-dependent analytic memory." Archive for Rational Mechanics and Analysis 248.115 (2024).
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