Exact Controllability to the Trajectories for a Nonlocal-in-time Semilinear Heat Equation

Huaman D.N. · Journal of Dynamical and Control Systems (2025) · DOI: 10.1007/s10883-025-09749-w

Resumen

In this paper, deals with the analysis of the internal control of a nonlocal-in-time semilinear heat equation. In our main result, we prove the exact controllability to the trajectories with distributed controls, locally supported in space. The main ingredients of the proof are an appropriate observability inequality of Carleman, a compactness-uniqueness argument, and Kakutani’s Fixed-Point Theorem in a suitable functional setting. Also, the null controllability with fewer hypotheses of term nonlinear, other possible extensions, and open problems on the nonlocal-in-time semilinear equation are presented. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

Instituciones: Universidad Nacional Agraria La Molina