CONTROLLABILITY OF THE BURGERS
EQUATION UNDER THE INFLUENCE OF
IMPULSES, DELAY AND NONLOCAL CONDITIONS
Cosme Duque1, Jahnett Uzcátegui2,
Hugo Leiva3, Oscar Camacho4
1,2 Universidad de Los Andes
Departamento de Matemáticas
Mérida - 5101 - VENEZUELA
3 Universidad Yachay Tech
San Miguel de Urcuqui, Imbabura - Ecuador
Ibarra - 100150 - ECUADOR
4Escuela Politécnica Nacional, Quito, Ecuador
Quito - 170109 - ECUADOR

Abstract

In the case of the Burges equation, this work proves the following conjecture: impulses, delays, and nonlocal conditions, under some assumptions, do not destroy some posed system qualitative properties since they are themselves intrinsic to it. we verified that the property of controllability is robust under this type of disturbances. Specifically, we prove that the interior approximate controllability of the linear heat equation is not destroyed if we add impulses, nonlocal conditions, and a nonlinear perturbation with delay in the state. This is done by using new techniques avoiding fixed point theorems employed by A.E. Bashirov et al. In this case the delay helps us to prove the approximate controllability of this system by pulling back the control solution to a fixed curve in a short time interval, and from this position, we are able to reach a neighborhood of the final state in time $\tau$ by using the fact that the corresponding linear heat equation is approximately controllable on any interval $[t_0, \tau]$, $0 < t_0 < \tau$.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 4
Year: 2020

DOI: 10.12732/ijam.v33i4.2

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