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Approximate Controllability of Non-autonomous Evolution System with Nonlocal Conditions

  • Pengyu ChenEmail author
  • Xuping Zhang
  • Yongxiang Li
Article
  • 59 Downloads

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.

Keywords

Approximate controllability Non-autonomous evolution equation Nonlocal conditions Evolution family Resolvent operator 

Mathematics Subject Classification (2010)

34K30 34K35 93B05 

Notes

Funding Information

This research was financially supported by the National Natural Science Foundation of China (No. 11501455), the National Natural Science Foundation of China (No. 11661071), and the Key Project of Gansu Provincial National Science Foundation (No. 1606RJZA015).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNorthwest Normal UniversityLanzhouPeople’s Republic of China

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