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arXiv · 2106.16001

Optimal control of linear non-local parabolic problems with an integral kernel

Umberto Biccari·Víctor Hernández-Santamaría·Loic Louison·Abdennebi Omrane
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Abstract

We consider a linear non-local heat equation in a bounded domain $\Omega\subset\mathbb{R}^d$, $d\geq 1$, with Dirichlet boundary conditions, where the non-locality is given by the presence of an integral kernel. Motivated by several applications in biological systems, in the present paper we study some optimal control problems from a theoretical and numerical point of view. In particular, we will employ the classical low-regret approach of J.-L. Lions for treating the problem of incomplete data and provide a simple computational implementation of the method. The effectiveness of the results are illustrated by several examples.

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Umberto Biccari, Víctor Hernández-Santamaría, Loic Louison, Abdennebi Omrane. 2021-06-30. Optimal control of linear non-local parabolic problems with an integral kernel. https://arxiv.org/abs/2106.16001

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