An Introduction to the Hyperbolic Diffusion Equation.

The paper is a synopsis of the basic premises of the hyperbolic form of the diffusion equation, collected from not readily accessible references. The premises are introduced in simplified form for application by meteorologists. The Markov process in phase space and the Lagrangian-Eulerian transform are discussed. Derivations of the hyperbolic equation, one from momentum consideration and one using a Markov process, are presented. Finally, the hyperbolic and the parabolic forms are compared. The hyperbolic diffusion equation offers advantages over the classical parabolic equation in the possibility of obtaining exact solutions and in the realistic physical assumptions under which it is derived. Author