Average Sentinel for a Heat Equation with Incomplete data
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Date
2024
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University of Oum El Bouaghi
Abstract
Identification problems consist of finding the causes of a phenomenon based on observation, and resolving this type of problem is done through experimental measurement. in this work, we propose to study a class of problems governed by a parabolic equation with incomplete data. For this purpose, we use the concept of sentinels introduced by (j. l. Lions), which is the most commonly used strategy, involving obtaining information about the causes from a weighted average of the observation. we then prove the existence of the average sentinel function by solving a zero-average controllability problem with control constraints. next, we are concerned with identifying pollution terms present in the heat equation with missing data.
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Keywords
Average sentinel; Identification method; Average observability