In this paper we give some sufficient conditions, which do ensure the existence and uniqueness of a compact almost automorphic solution to some hyperbolic differential equations. As an illustration, we study the existence and uniqueness of almost automorphic solutions to a one-dimensional heat equation with small delays.
Toka Diagana. "On the Existence of Almost Automorphic Solutions to Some Abstract Hyperbolic Differential Equations." Bull. Belg. Math. Soc. Simon Stevin 17 (2) 219 - 234, april 2010. https://doi.org/10.36045/bbms/1274896201