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<p>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.</p>

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Control of the Fisher-Stefan System

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月29日

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  • Idriss Boutaayamou,
  • Fouad Et-tahri,
  • Lahcen Maniar,
  • Francisco Periago

摘要

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.