  In this paper, we consider a linear heat equation with constant coefficients
and a single constant delay. Such equations are commonly used to model and
study various problems arising in ecology and population biology when
describing the temporal evolution of human or animal populations accounting for
migration, interaction with the environment and certain aftereffects caused by
diseases or enviromental polution, etc. Whereas dynamical systems with lumped
parameters have been addressed in numerous investigations, there still remain a
lot of open questions for the case of systems with distributed parameters,
especially when the delay effects are incorporated. Here, we consider a general
non-homogeneous one-dimensional heat equation with delay in both higher and
lower order terms subject to non-homogeneous initial and boundary conditions.
For this, we prove the unique existence of a classical solution as well as its
continuous dependence on the data.
