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This is a Quantitative Study study.

October 17, 2025Open Access

Controllability under positivity constraints for non-linear and non-local parabolic PDEs

Key Points

The study reveals important controllability results for a parabolic PDE under positivity constraints.
Key findings include local results in Holder spaces, with implications for control strategies.
The research employs tools like Carleman inequalities and stability methods to establish its findings.
Positivity constraints are shown to impact the minimal controllability time for the system.

Abstract

This article studies the control of a non-local and non-linear parabolic PDE. The tools to develop the control study are: regularity in Holder spaces, parabolic regularity, Carleman and Observability inequalities, compactness, stability and the Kakutani Fixed Point method. We obtain three results about controllability. first, local results in H\"older spaces; second, restriction on the control signal with target trajectories; and third, positivity of the minimal controllability time. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2025/96/abstr.html

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Cite This Study

Miguel R. Núñez-Chávez (Tue,) studied this question.

synapsesocial.com/papers/68f199c5de32064e504dcf1f https://doi.org/https://doi.org/10.58997/ejde.2025.96

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