Approximate controllability of a Sobolev type impulsive functional evolution system in Banach spaces

Arora Sumit; Mohan Manil T.; Dabas Jaydev

doi:10.3934/mcrf.2020049

Article Contents

2021, Volume 11, Issue 4: 857-883. Doi: 10.3934/mcrf.2020049 open access

This issue Previous Article Stochastic maximum principle for problems with delay with dependence on the past through general measures Next Article Stability of N-D transmission problem in viscoelasticity with localized Kelvin-Voigt damping under different types of geometric conditions

Approximate controllability of a Sobolev type impulsive functional evolution system in Banach spaces

1.
Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India
2.
Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

^*Corresponding author: Jaydev Dabas
^*Corresponding author: Jaydev Dabas

Received: March 31, 2020

Revised: June 30, 2020

Early access: November 2020

Published: December 2021

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Abstract

In this paper, we investigate the approximate controllability problems of certain Sobolev type differential equations. Here, we obtain sufficient conditions for the approximate controllability of a semilinear Sobolev type evolution system in Banach spaces. In order to establish the approximate controllability results of such a system, we have employed the resolvent operator condition and Schauder's fixed point theorem. Finally, we discuss a concrete example to illustrate the efficiency of the results obtained.

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Mathematics Subject Classification: 34K06, 34A12, 37L05, 93B05.

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