Moving Sentinels for a Nonlinear Heat Equation with Memory

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DOI: https://doi.org/10.28924/2291-8639-24-2026-352
Published: Oct 15, 2026
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Fouzia. Segueni, Abdennebi. Omrane, Moving Sentinels for a Nonlinear Heat Equation with Memory, Int. J. Anal. Appl., 24 (2026), 352.

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Fouzia. Segueni, Abdennebi. Omrane

Abstract

We consider a nonlinear heat equation with memory terms and missing data. Motivated by its numerous applications in captivating physical phenomena and engineering fields and other complex systems, the problem presents considerable challenges due to the presence of a memory integral term and a moving control, and in addition, due to the presence of incomplete data (pollution terms and incomplete data). This paper investigates the existence of insensitizing controls sentinel for this equation. We show that finding a moving sentinel is equivalent to solving a memory-type null-controllability problem. Our approach relies on the application of duality arguments to obtain an observability inequality, using Carleman estimates.

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