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Journal of Dynamical and Control Systems

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29-11-2018

Approximate Controllability of Non-autonomous Evolution System with Nonlocal Conditions

Published in: Journal of Dynamical and Control Systems | Issue 1/2020

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Abstract

In this article, we are concerned with the existence of mild solutions as well as approximate controllability for a class of non-autonomous evolution system of parabolic type with nonlocal conditions in Banach spaces. Sufficient conditions of existence of mild solutions and approximate controllability for the desired problem are presented by introducing a new Green’s function and constructing a control function involving Gramian controllability operator. Some sufficient conditions of approximate controllability are formulated and proved here by using the resolvent operator condition. The discussions are based on Schauder’s fixed-point theorem as well as the theory of evolution family. An example is also given to illustrate the feasibility of our theoretical results.

next article Periodic Solutions of a Class of Non-autonomous Discontinuous Second-Order Differential Equations

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Title: Approximate Controllability of Non-autonomous Evolution System with Nonlocal Conditions
Publication date: 29-11-2018
Published in: Journal of Dynamical and Control Systems / Issue 1/2020
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI: https://doi.org/10.1007/s10883-018-9423-x

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