Control of the Fisher-Stefan system

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.

💡 Research Summary

The paper investigates the exact controllability of trajectories for a one‑dimensional Fisher‑Stefan problem, which couples the classical Fisher–KPP reaction‑diffusion equation with a Stefan-type moving boundary condition. The authors consider the system on a time interval (