When two microemulsions are put in contact in the gravity field along a horizontal contact line, cross-diffusion can trigger the transport of one species in the presence of a gradient in concentration of another species. We show here theoretically that such cross-diffusion effects can induce buoyancy-driven convective instabilities at the interface between two solutions of different composition...

Non-linear reaction-diffusion processes with cross-diffusion in two-dimensional, anisotropic media are analyzed by means of an implicit, iterative, time-linearized approximate factorization technique as functions of the anisotropy of the heat and species diffusivity tensors, the Soret and Dufour cross-diffusion effects, and five types of boundary conditions. It is shown that anisotropy and cros...

A strongly coupled cooperative parabolic system, which describes fecally-orally epidemic model with cross-diffusion in a heterogeneous environment, was formulated and analyzed. The basic reproduction number R0 , which serves as a threshold parameter that predicts whether the coexistence will exist or not, is introduced by the next infection operator and the related eigenvalue problems. By apply...

We consider Taylor-Aris dispersion in columns of nearly rectangular cross section of large aspect ratio. We generalize the results of [1] and [2] who showed that the effective diffusion rate for perfectly rectangular cross sections is remarkably different than the diffusion rate between two parallel plates – as the aspect ratio goes to infinity, the effective diffusion rate does not approach th...

This paper is a continuation of Part I 1 . In Section 3 of Part I, using the energy estimate and bootstrap arguments, the global existence of solutions for a Holling type III cross-diffusion predator-prey model with stage-structure has been discussed when the space dimension be less than 6. However, to obtain the L∞ estimate for the population density w of predator species, there is not cross-d...

We investigate the effects of cross-diffusion on propagating waves in an activator-inhibitor system. The model consists of a piecewise linear approximation of FitzHugh-Nagumo kinetics and a cross-diffusion term for either the activator or the inhibitor. We obtain exact analytic solutions for traveling fronts and solitary pulses and discuss the corresponding speed diagrams. A detailed comparison...

An analysis of traveling wave solutions of pure cross-diffusion systems, i.e., systems that lack reaction and self-diffusion terms, is presented. Using the qualitative theory of phase plane analysis the conditions for existence of different types of wave solutions are formulated. In particular, it is shown that family of wave trains is a generic phenomenon in pure cross-diffusion systems. The r...