Ravikumar, Kasinathan and Anguraj, Annamalai
(2021)
*APPROXIMATE CONTROLLABILITY OF A NON-AUTONOMOUS EVOLUTION EQUATION IN BANACH SPACES.*
NUMERICAL ALGEBRA, CONTROL AND OPTIMIZATION, 11 (3).
pp. 461-485.

2155-3289_2021_3_461.pdf - Published Version

Download (516kB)

## Abstract

In this paper, we consider a class of non-autonomous nonlinear evolution equations 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 a example of a non-autonomous, nonlinear diffusion equation in Banach spaces

to validate the results we obtained.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | words and phrases. Non-autonomous evolution equations, Approximate controllability, Schauder’s fixed point theorem, Resolvent operators |

Divisions: | PSG College of Arts and Science > Department of Mathematics |

Depositing User: | Mr Team Mosys |

Date Deposited: | 06 Jun 2022 05:37 |

Last Modified: | 06 Jun 2022 05:37 |

URI: | http://ir.psgcas.ac.in/id/eprint/1213 |