Electron. J. Differential Equations, Vol. 2025 (2025), No. 96, pp. 1-35.

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

Miguel R. Nunez-Chavez

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.

Submitted May 29, 2025. Published October 14, 2025.
Math Subject Classifications: 93C20, 35K55, 93C10, 93B05, 93B07.
Key Words: Nonlocal parabolic equation; nonlinear parabolic equation; exact controllability to trajectories; control with restriction; positivity time of the control.
DOI: 10.58997/ejde.2025.96

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Miguel R. Nuñez-Chávez
UFMT- Federal University of Mato Grosso, ICET
Department of Mathematics, 78060-900
Cuiabá, MT, Brazil email: miguel.chavez@ufmt.br

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