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

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.