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Non-local Equations For Concentration Waves In Reacting Diffusion Systems


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A. M. Brener, M. A. Serimbetov & L. M. Musabekova


This paper presents the equations modelling concentration waves in reacting diffusion systems. We show that under the highly general assumptions concerning the nature of space non-locality of relations between thermodynamic fluxes and forces the governing transfer equation acts in the form of the modified Witham’s integro-differential equation. In contradistinction to the known Witham’s equation the one obtained is heterogeneous under the presence of heat and mass sources. It is shown that transfer processes with consideration of dependencies of transfer coefficients on the coordinates and chemical potentials can also be described by an equation of the same type. In the paper the pre-conditions and computations leading to the mentioned non-linear equation have been adduced. The important peculiarity of the equation obtained is the possibility to describe the propagation of dispersing running waves and moving wave fronts in media with complex structure. Within the limits of this equation’s characteristic analysis there proved to be a successful method of the investigation of the solitary concentration waves by the \“classic way”, i.e. as a result of interaction between the non-linear phenomena and dispersion. 1 Introduction It is imperative under calculating heat and mass transfer processes in media with complex internal structure and various kinds of interaction between medium elements to account for both the non-linear and the non-local phenomena. The problem to describe such processes is too complex and far from the complete solution. In this connection the model approach, which under the successful choice of the main governing factors and appropriate parameters allows one to obtain model transfer equations, is relevant.