The purpose of this work is to discuss the fundamental theory for a of partial functional differential equations with a non dense domain. We assume that the linear part is not necessarily densely defined and satisfies the known Hille-Yosida condition. We suppose that the nonlinear part is locally Lipschitz continuous. We prove the existence of mild and strict solutions. When the solutions are globally defined, we give a linearized principal near an equilibrium. We investigate the stability and the asymptotic behavior of solutions of the linear equations. We prove that the behavior of solutions is completely obtained by the so-called characteristic equation. We study the existence of bounded solutions for nonhomogeneous equation. We prove the existence of periodic or almost periodic solutions when the solution semigroup of the linear equation is hyperbolic. Finally, we propose to study the stability for a one dimensional reaction diffusion model with delay arising in physical systems.