Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 212, pp. 1-11.

Title: Almost automorphic mild solutions of hyperbolic evolution equations
       with stepanov-like almost automorphic forcing term
        
Authors: Indira Mishra      (Indian Institute of Tech., Kanpur, India)
         Dhirendra Bahuguna (Indian Institute of Tech., Kanpur, India)

Abstract:
 This article concerns the existence and uniqueness of almost automorphic
 solutions to the semilinear parabolic boundary differential equations
 $$\displaylines{
 x'(t)=A_mx(t)+f(t,x(t)), \quad t\in \mathbb{R}, \cr
 Lx(t)=\phi(t,x(t)), \quad t\in \mathbb{R},
 }$$
 where $A:=A_m|_{\ker L}$ generates a hyperbolic analytic semigroup on a Banach
 space $X$, with Stepanov-like almost automorphic nonlinear term, defined
 on some extrapolated space $X_{\alpha-1}$, for $0<\alpha<1$ and $\phi$
 takes values in the boundary space $\partial X$. 

Submitted December 1, 2011. Published November 27, 2012.
Math Subject Classifications: 34K06, 34A12, 37L05.
Key Words: Almost automorphic; evolution equation; hyperbolic semigroups;  
           extrapolation spaces; interpolation spaces;
	   neutral differential equation; mild solution.