On Uniform h-stability of Non-autonomous Evolution Equations in Banach Spaces

In this paper, we are concerned with the global existence of mild solutions as well as uniform h-stability for non-autonomous evolution equations in a Banach space, where the operators in linear part (possibly unbounded) depend on time t and generate an evolution family. Under some estimates on the perturbation terms, we discuss the global uniform h-stability, the uniform h-stability and the global practical uniform h-stability using Gronwall integral inequalities. Some examples are provided to show the validity of the obtained results.