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

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 $\Gamma\gg 1$ 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 $\Gamma$. The pre-exponential factor in the expression for the concentration has been determined in the leading approximation in the small parameter $\Gamma^{-1}$. An analogy with geometrical optics and semiclassical approximation in quantum mechanics has been demonstrated.