Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 49, pp. 1-19.

Title: Evolution equations in generalized Stepanov-like pseudo almost 
       automorphic spaces

Author: Toka Diagana (Howard Univ., Washington, DC, USA)

Abstract:
 In this article, first we introduce and study the concept of 
 $\mathbb{S}_{\gamma}^p$-pseudo  almost automorphy 
 (or generalized Stepanov-like pseudo almost automorphy),
 which is more general than the notion of Stepanov-like pseudo
 almost automorphy due to Diagana. We next study the existence of solutions
 to some classes of nonautonomous differential
 equations of Sobolev type in $\mathbb{S}_{\gamma}^p$-pseudo almost 
 automorphic spaces.  To illustrate our abstract result,
 we will study the existence and  uniqueness of a pseudo almost 
 automorphic solution to the heat equation with a negative 
 time-dependent diffusion coefficient.
  
Submitted February 1, 2012. Published March 27, 2012.
Math Subject Classifications: 58D25, 58D25, 43A60, 35B15, 42A75, 37L05.
Key Words: Pseudo almost automorphic;  Stepanov-like; almost automorphic.