Approximate controllability of a non-autonomous evolution equation in Banach spaces
Optimization and Control
2020-04-24 v2
Abstract
In this paper, we consider a non-autonomous nonlinear evolution equation in separable, reflexive Banach spaces. First, we consider a linear problem and establish the approximate controllability results by finding a feedback control with the help of an optimal control problem. We then establish the approximate controllability results for a semilinear differential equation in Banach spaces using the theory of linear evolution systems, properties of resolvent operator and Schauder's fixed point theorem. Finally, we provide an example of a non-autonomous, nonlinear diffusion equation in Banach spaces to validate the results we obtained.
Cite
@article{arxiv.2004.10460,
title = {Approximate controllability of a non-autonomous evolution equation in Banach spaces},
author = {K. Ravikumar and M. T. Mohan and A. Anguraj},
journal= {arXiv preprint arXiv:2004.10460},
year = {2020}
}