Internal null controllability for the one-dimensional heat equation with dynamic boundary conditions

2024/04/02 by El Mustapha Ait Ben Hassi, Hassi, El Mustapha Ait Ben, Mariem Jakhoukh +5
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2404.01539

openalex publication_date 2024/04/02 · openalex created_date 2024/04/05 · openalex updated_date 2026/07/28

Abstract

The primary focus of this paper is to establish the internal null controllability for the one-dimensional heat equation featuring dynamic boundary conditions. This achievement is realized by introducing a new Carleman estimate and an observability inequality for the corresponding backward system. In conclusion, the paper includes a set of numerical experiments that serve to confirm the validity of the theoretical findings and underscore the effectiveness of the designed control with a minimal L2-norm.

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