Functional differential equations and one-dimensional distortionless propagation

One-dimensional propagation phenomena of physics and technology are described by boundary value problems for hyperbolic partial differential equations in one space dimension. Since the paper of J. Bernoulli published in 1728, functional equations are usually associated with such problems, the best known in the last decades being the neutral differential equations with deviated arguments. The distortionless propagation corresponds to the case of the equations with pointwise (lumped) time delays. The present paper will consider some applications of these equations in nuclear and power engineering, engineering mechanics, hydraulics. The basic model validation steps (basic theory, invariant sets, inherent stability) are discussed.