Impulsive semilinear heat equation with delay in control and in state

In this paper, we prove the interior approximate controllability of the impulsive semilinear heat equation with delay in control and in state by proving first that the linear heat equation with delay in control is approximately controllable. After that, we add impulses and a nonlinear perturbation w...

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Bibliographic Details
Published in:Asian journal of control 2020-05, Vol.22 (3), p.1075-1089
Main Authors: Camacho, Oscar, Leiva, Hugo
Format: Article
Language:English
Subjects:
Controllability
Delay
Fixed points (mathematics)
Hilbert space
impulsive semilinear heat equation with delay in control
interior approximate controllability
Perturbation
Rothe's fixed point
Stability
strongly continuous semigroups
Thermodynamics
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Summary:In this paper, we prove the interior approximate controllability of the impulsive semilinear heat equation with delay in control and in state by proving first that the linear heat equation with delay in control is approximately controllable. After that, we add impulses and a nonlinear perturbation with delay in state, and using Rothe's fixed point theorem, we prove that the interior approximate controllability of the impulsive semilinear system. Finally, we present some open problems and a possible general framework to study the controllability of impulsive semilinear diffusion process in Hilbert spaces with delay in control and in state.
ISSN:1561-8625
1934-6093
DOI:10.1002/asjc.2017