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SAMPLING OBSERVABILITY FOR HEAT EQUATIONS WITH MEMORY
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DOI：10.1137/24M1712151.png)
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Abstract
En 中文
This paper studies the sampling observability for the heat equations with memory in the lower-order term, where the observation is conducted at a finite number of time instants and on a small open subset at each time instant. We present a two-sided sampling observability inequality and give a sharp sufficient condition to ensure the aforementioned inequality. We also provide a method to select the time instants and then to design the observation regions, based on a given memory kernel, such that the abovementioned inequality holds for these time instants and observation regions. Additionally, we demonstrate that the positions of these time instants depend significantly on the memory kernel.
Keywords:
heat equations with memory
observability
sampling
geometric characterization of observation sets
Journal
S
IF:
2.4
Papers:
31
Citations:
0