Non-autonomous Evolution Equations of Parabolic Type with Non-instantaneous Impulses

  • Pengyu ChenEmail author
  • Xuping Zhang
  • Yongxiang Li


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.


non-autonomous evolution equation parabolicity condition non-instantaneous impulse evolution family mild solution 

Mathematics Subject Classification

34K45 35R12 65J08 



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Authors and Affiliations

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

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