Null controllability of linear and semilinear nonlocal heat equations with integral kernel

2017/11/13 by Umberto Biccari, Biccari, Umberto, Víctor Hernández-Santamaría +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1711.04690

openalex publication_date 2017/11/13 · openalex created_date 2018/06/13 · openalex updated_date 2026/07/28

Abstract

We consider a linear nonlocal heat equation in a bounded domain Ω⊂ℝ^d with Dirichlet boundary conditions. The non-locality is given by the presence of an integral kernel. We analyze the problem of controllability when the control acts on an open subset of the domain. It is by now known that the system is null-controllable when the kernel is time-independent and analytic or, in the one-dimensional case, in separated variables. In this paper, we relax this assumption and we extend the result to a more general class of kernels. Moreover, we get explicit estimates on the cost of null-controllability that allow us to extend the result to some semilinear models.

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