Boundary null controllability for the heat equation with dynamic boundary conditions

2022/06/21 by S. E. Chorfi, Chorfi, S. E., G. El Guermai +5 · 1 citation
Computer Science · Engineering · Mathematics · #93B05 (Primary) 35K05 #93B07 (Secondary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2206.10701

openalex publication_date 2022/06/21 · openalex created_date 2022/12/14 · openalex updated_date 2026/07/28

Abstract

In this paper, we are concerned with the boundary controllability of heat equation with dynamic boundary conditions. More precisely, we prove that the equation is null controllable at any positive time by means of a boundary control supported on an arbitrary subboundary. The proof of the main result combines a new boundary Carleman estimate and some regularity estimates for the adjoint system, with an explicit dependence with respect to the final time. This technique allows us to overcome a new difficulty that arises when absorbing a normal derivative term.

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