TY - JOUR

T1 - Controllability of the Burgers equation under the influence of impulses, delay and nonlocal conditions

AU - Duque, Cosme

AU - Uzcátegui, Jahnett

AU - Leiva, Hugo

AU - Camacho, Oscar

N1 - Publisher Copyright:
© 2020 Academic Publications.

PY - 2020

Y1 - 2020

N2 - 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 them-selves intrinsic to it. we verified that the property of controllability is robust under this type of disturbances. Specifically, we prove that the interior ap-proximate 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 em-ployed 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 τ by using the fact that the cor-responding linear heat equation is approximately controllable on any interval [t0, τ], 0 < t0 < τ.

AB - 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 them-selves intrinsic to it. we verified that the property of controllability is robust under this type of disturbances. Specifically, we prove that the interior ap-proximate 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 em-ployed 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 τ by using the fact that the cor-responding linear heat equation is approximately controllable on any interval [t0, τ], 0 < t0 < τ.

KW - Impulsive burgers equation with delays and nonlocal conditions

KW - Interior approximate controllability

KW - New technique

KW - Strongly continuous semigroups

UR - http://www.scopus.com/inward/record.url?scp=85090837642&partnerID=8YFLogxK

U2 - 10.12732/ijam.v33i4.2

DO - 10.12732/ijam.v33i4.2

M3 - Artículo

AN - SCOPUS:85090837642

SN - 1311-1728

VL - 33

SP - 573

EP - 583

JO - International Journal of Applied Mathematics

JF - International Journal of Applied Mathematics

IS - 4

ER -