Approximate controllability of nonlocal problem for non-autonomous stochastic evolution equations

Pengyu Chen; Xuping Zhang

doi:10.3934/eect.2020076

Article Contents

2021, Volume 10, Issue 3: 471-489. Doi: 10.3934/eect.2020076

This issue Previous Article A remark on the attainable set of the Schrödinger equation Next Article New results on controllability of fractional evolution systems with order

$ \alpha\in (1,2) $

Approximate controllability of nonlocal problem for non-autonomous stochastic evolution equations

Pengyu Chen^, and
Xuping Zhang

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

^* Corresponding author: Pengyu Chen
^* Corresponding author: Pengyu Chen

Received: October 31, 2019

Revised: March 31, 2020

Early access: June 2020

Published: September 2021

The first author is supported by NSF of China (No. 11661071), Project of NWNU-LKQN2019-3 and China Scholarship Council (No. 201908625016); The second author is supported by the Science Research Project for Colleges and Universities of Gansu Province (No. 2019B-047) and Project of NWNU-LKQN2019-13

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Abstract

In this paper, we are considered with approximate controllability for a class of non-autonomous stochastic evolution equations of parabolic type with discrete nonlocal initial conditions. Some new results about existence of mild solutions as well as approximate controllability are established under more natural conditions on nonlinear functions and control operator by introducing a new Green function and using the theory of evolution family, Schauder fixed point theorem and the resolvent operator condition. At last, as a sample of application, these results are applied to a class of non-autonomous stochastic partial differential equation of parabolic type with discrete nonlocal initial conditions. The results obtained in this paper is a supplement to the existing literature and essentially extends some existing results in this area.

Keywords:

Approximate controllability,
Non-autonomous stochastic evolution equations,
Nonlocal initial conditions,
Wiener process,
Evolution family,
Resolvent operator.

Mathematics Subject Classification: Primary: 34F05, 60H15; Secondary: 34K35, 93B05.

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