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Non-autonomous parabolic evolution equations with non-instantaneous impulses governed by noncompact evolution families

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Abstract

In this paper, we study the initial value problem to a class of non-autonomous parabolic evolution equations with non-instantaneous impulses in Banach spaces, where the operators in linear part (possibly unbounded) depend on time t and generate an noncompact evolution family. Some new existence results of piecewise continuous mild solutions are established under more weaker conditions. At last, as a sample of application, these results are applied to a class of non-autonomous partial differential equation of parabolic type with non-instantaneous impulses. The results obtained in this paper are a supplement to the existing literature and essentially extend some existing results in this area.

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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

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  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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Research supported by National Natural Science Foundation of China (No. 11501455), National Natural Science Foundation of China (No. 11661071) and Doctoral Research Fund of Northwest Normal University (No. 6014/0002020209).

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Chen, P., Zhang, X. & Li, Y. Non-autonomous parabolic evolution equations with non-instantaneous impulses governed by noncompact evolution families. J. Fixed Point Theory Appl. 21, 84 (2019). https://doi.org/10.1007/s11784-019-0719-6

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  • DOI: https://doi.org/10.1007/s11784-019-0719-6

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