A population equation with diffusion

In this paper we discuss a population equation with diffusion. It is different from the equation proposed, for example, in [K.J. Engel, R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, 2000] or in [J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, 1996] so far as it combines diffusion with delay.We explain the origin of this equation and study it with the theory developed by G. Fragnelli and G. Nickel (Differential Integral Equations 16 (2003) 327–348) and G. Fragnelli (Abstract Appl. Anal., in press).  2003 Elsevier Inc. All rights reserved.