Controllability of impulsive semilinear stochastic heat equation with delay
type: Item
instance of: scholarly article
title: Controllability of impulsive semilinear stochastic heat equation with delay
zbMATH Open document ID: 1468.35201
DOI: 10.1155/2020/2515160
author: Hugo Leiva
author: Zoraida Sivoli
author: Miguel Narváez
published in: International Journal of Differential Equations
publication date: 2021-05-19T00:00:00Z
review text: Summary: LaSalle wrote the following: ``it is never possible to start the system exactly in its equilibrium state, and the system is always subject to outside forces not taken into account by the differential equations. The system is disturbed and is displaced slightly from its equilibrium state. What happens? Does it remain near the equilibrium state? This is stability. Does it remain near the equilibrium state and in addition tend to return to the equilibrium? This is asymptotic stability.'' Continuing with what LaSalle said, we conjecture that real-life systems are always under the influence of impulses, delays, memory, nonlocal conditions, and noises, which are intrinsic phenomena no taken into account by the mathematical model that is representing by a differential equation. For many control systems in real life, delays, impulses, and noises are natural properties that do not change their behavior. So, we conjecture that, under certain conditions, the abrupt changes, delays, and noises as perturbations of a system do not modify certain properties such as controllability. In this regard, we prove the interior \(S^\ast \)-controllability of the semilinear stochastic heat equation with impulses and delay on the state variable, and this is done by using new techniques avoiding fixed point theorems employed by Bashirov et al.
Mathematics Subject Classification ID: 35Q79
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35K58
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 35R07
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 7349540
zbMATH Keywords: stochastic heat equation
zbMATH Keywords: Controllability
zbMATH Keywords: delay
Wikidata QID: Q115243873
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/2515160
OpenAlex ID: W3117116813
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description: scientific article; zbMATH DE number 7349540