Asymptotic approach to the description of nonclassical transport processes. Fermat’s principle

Abstract

A method has been proposed to calculate the concentration distribution at asymptotically long distances from a source of impurity in a medium including long-scale heterogeneities. It has been found that the exponent Γ ≫ 1 in an expression for the concentration satisfies a nonlinear equation with first-order partial derivatives. This has allowed using the variational principle to calculate the function Γ. The pre-exponential factor in the expression for the concentration has been determined in the leading approximation in the small parameter Γ⁻¹. An analogy with geometrical optics and semiclassical approximation in quantum mechanics has been demonstrated.