摘要：In this paper, the parabolic evolution equation u ′ ( t ) + A ( t ) u ( t ) = f ( t ) $u'(t)+A(t)u(t)=f(t)$ in a reflexive real Banach space is considered. Assuming strong monotonicity, pseudo almost automorphy and other appropriate conditions of the operators A ( t ) $A(t)$ and Stepanov-like pseudo almost automorphy of the forced term f ( t ) $f(t)$ , we obtain the Stepanov-like pseudo almost automorphy of the solution to the evolution equation by using the almost automorphic component equation method. This paper extends a known result in the case where A ( ⋅ ) $A( ot)$ and f are almost automorphic in certain senses. Finally, a concrete example is given to illustrate our results.
