Asymptotical almost periodicity of solutions to the Keller-Segel system on real hyperbolic manifolds

In this article, we shall study the Keller-Segel system on a real hyperbolic space which is one class of Riemannian manifolds with Ricci curvature -1. We prove the existence, uniqueness of asymptotically almost periodic solutions for the linear equations by using dispersive and smoothing properties of the heat semigroup.