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Approximate Controllability of Non-autonomous Evolution System with Nonlocal Conditions

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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.

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Funding

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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Authors and Affiliations

  1. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Pengyu Chen, Xuping Zhang & Yongxiang Li

Authors
  1. Pengyu Chen
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  2. Xuping Zhang
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  3. Yongxiang Li
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Correspondence to Pengyu Chen.

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Chen, P., Zhang, X. & Li, Y. Approximate Controllability of Non-autonomous Evolution System with Nonlocal Conditions. J Dyn Control Syst 26, 1–16 (2020). https://doi.org/10.1007/s10883-018-9423-x

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  • DOI: https://doi.org/10.1007/s10883-018-9423-x

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