Work

Control of the Fisher-Stefan System

Year: 2026

Type: article

Abstract: This paper addresses the exact controllability of trajectories in the one-dimensional Fisher-Stefan problem—a reaction-diffusion equation that models the spatial propagation of biological, chemical, or physical populations within a free-end domain, governed by Stefan’s law. We establish the local exact controllability of the trajectories by reformulating the problem as the local null controllability of a nonlinear system with distributed controls. Our approach leverages the Lyusternik-Graves theorem to achieve local inversion, leading to the desired controllability result. Finally, we illustrate our theoretical findings through several numerical experiments based on the physics-informed neural networks (PINNs) approach.

Source: Communications on Applied Mathematics and Computation

DOI: 10.1007/s42967-026-00582-x

Authors: Idriss Boutaayamou, Fouad Et-tahri, Lahcen Maniar, Francisco Periago

Institutions: Université Ibn Zohr, Cadi Ayyad University, Université Mohammed VI Polytechnique, Universidad Politécnica de Cartagena

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Ministry of Science and Technology, Fundación Séneca, Universidad Politécnica de Cartagena