Approximate distributed controllability of nonlocal Rayleigh beam
نویسندگان
1 School of Engineering, Damghan University, Damghan, Iran.
2 School of Mathematics and Computer Sciences, Damghan University, Damghan, P.O. Box 36715-364, Iran.
3 School of Mathematics and Computer Sciences, Damghan University, Damghan, P.O. Box 36715-364, Iran.
doi
10.22034/cmde.2020.29618.1434چکیده
This paper investigates the distributed controllability of nonlocal Rayleigh beam. The mathematical problem is formulated as an abstract differential equation. It is shown that a sequence of eigenfunction of nonlocal Rayleigh beam forms Riesz basis. Based on Riesz basis properties and theory of abstract differential equation, it is proved that a vibrating nonlocal Rayleigh beam is approximately controllable under suitable distributed control force while it is not exponentially stable.
