Abstract
In this paper, we study the Cauchy problem to a class of non-autonomous evolution equations of parabolic type with non-instantaneous impulses in Banach spaces, where the operators in linear part (possibly unbounded) depend on time t and generate an evolution family. New existence result of piecewise continuous mild solutions is established under more weaker conditions. At last, as a sample of application, the abstract result is applied to a class of non-autonomous partial differential equation of parabolic type with non-instantaneous impulses. The result obtained in this paper is a supplement to the existing literature and essentially extends some existing results in this area.
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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 Evolution Equations of Parabolic Type with Non-instantaneous Impulses. Mediterr. J. Math. 16, 118 (2019). https://doi.org/10.1007/s00009-019-1384-0
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DOI: https://doi.org/10.1007/s00009-019-1384-0
Keywords
- non-autonomous evolution equation
- parabolicity condition
- non-instantaneous impulse
- evolution family
- mild solution