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arXiv · 2503.23154

Control of the Fisher-Stefan system

Idriss Boutaayamou·Fouad Et-tahri·Lahcen Maniar·Francisco Periago
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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 to 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.

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Idriss Boutaayamou, Fouad Et-tahri, Lahcen Maniar, Francisco Periago. 2025-03-29. Control of the Fisher-Stefan system. https://arxiv.org/abs/2503.23154

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