Stepanov-like pseudo almost automorphic solution to a parabolic evolution equation

作者：Ji, Desheng^*; Lu, Yueming

来源：Advances in Difference Equations, 2015, 2015(1): 341.

DOI：10.1186/s13662-015-0667-4

• almost automorphic solution
• pseudo almost automorphic solution
• parabolic evolution equation
• monotone operators

In this paper, the parabolic evolution equation 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) and Stepanov-like pseudo almost automorphy of the forced term 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(center dot) and f are almost automorphic in certain senses. Finally, a concrete example is given to illustrate our results.

• 出版日期2015-10-29
• 单位黑龙江大学; 哈尔滨学院