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Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2024

Open Access Link: https://dcn.nat.fau.eu/wp-content/uploads/observability-for-heat-equations-with-memory.pdf


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. 

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Wang, G., Zhang, Y., & Zuazua Iriondo, E. (2024). Observability for heat equations with time-dependent analytic memory. (Unpublished, Submitted).


Wang, Gengsheng, Yubiao Zhang, and Enrique Zuazua Iriondo. Observability for heat equations with time-dependent analytic memory. Unpublished, Submitted. 2024.

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