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

Umberto Biccari, Víctor Hernández-Santamaría, Loic Louison, Abdennebi Omrane. Optimal control of linear non-local parabolic problems with an integral kernel. (2021)

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.

Read Full Paper

Arxiv: 2106.16001

Last updated on March 17, 2022

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Last Publications

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