CDS and Continuous Non Linear Media. The Principle of Maximum of Flows of Substance. Laplace Operator of CDS

Abstract

In the present section we shall show that with every CDS governed by the inclusion q ∈ f (q , U), q ∈ {q} a definite continous medium can be associated in which there takes place a propagation to a substationof, for example, heat, mass, charge etc. To be definite, we shall consider a heat transmitting stationary medium which occupies an n- dimensional space {q} = Rⁿ. The state of this medium will be described by a function of temperature distribution z = z (q, t), where q ∈ {q} and t denotes the time. For brevity, in the sequel we shall drop the argument t in writing this function.