Nonlinear Wave Model for Transport Phenomena in Media with Non-local Effects

Abstract

The purpose of the work is to establish and substantiate the prerequisites under which the modified Whitham equation can play the role of a transfer equation in physical-chemical systems and technological processes. The contribution of this work lie in the fact that the perturbed Whitham equation describing propagation of nonlinear waves in media with non-locality has been derived using the nonlinear relaxation function. It is shown that while deriving the equations of the Whitham type, the presence of the spatial non-locality of the medium can play a fundamental role. The paper also considers the issues of physical interpretation of the model under study. The principal presence of non-local effects in studied systems can be substantiated and obtained as a result of the presence of domains with a complexly organized spatial structure as well as in the presence of heat and mass sources. The new model submitted in the work can find application in methods for calculating the intensity of heat and mass transfer in complexly structured heterogeneous systems.