In this article we propose a unified framework in order to study reaction–diffusion systems containing self- and cross-diffusion using free energy approach. This naturally leads the formulation of an law, numerical method respecting discrete version latter. It constitutes alternative complements standard linear stability analysis, as it allows for nonlinear patterns, while monitoring evolution,...

The paper is devoted to the mathematical analysis of Cauchy problem for general cross-diffusion systems without any assumption about its entropic structure. A global existence result nonnegative solutions obtained by applying a classical Schauder fixed point theorem. proof upgraded enhancing regularity solution, namely gradient belongs space Lr((0,T)×Ω) some r>2. To this aim, Schauder's strateg...

In a reaction-diffusion system, diffusion can induce the instability of a uniform equilibrium which is stable with respect to a constant perturbation, as shown by Turing in 1950s. We show that cross-diffusion can destabilize a uniform equilibrium which is stable for the kinetic and self-diffusion reaction systems; on the other hand, cross-diffusion can also stabilize a uniform equilibrium which...

where ut = ∂u ∂t and ∆ =∑ni=1 ∂2 ∂xi is the usual Laplace operator, Ω is a bounded smooth domain in Rn, υ is the unit outer normal to ∂Ω, and u0 is a realvalued continuous function (not identically zero) representing the initial heat distribution. Here the boundary condition implies that (1) is an isolated system. It is well known that the solution u(x, t) of (1) becomes smooth as soon as t bec...

Coupled diffusion is observed in multicomponent liquid mixtures in which strong thermodynamic interactions occur. This phenomenon is described by cross terms in the matrix of multicomponent diffusion coefficients. This paper reports a theoretical analysis on the relative role of thermodynamic factors and Onsager cross-coefficients on cross-diffusion coefficients relevant to ternary mixtures con...

We study a parabolic population model in the full space and prove the global in time existence of a weak solution. This model consists of two strongly coupled diffusion equations describing the population densities of two competing species. The system features intrinsic growth, interand intra-specific competition of the species, as well as diffusion, cross-diffusion and self-diffusion, and drif...

We study a parabolic population model in the full space and prove the global in time existence of a weak solution. This model consists of two strongly coupled diffusion equations describing the population densities of two competing species. The system features intrinsic growth, interand intra-specific competition of the species, as well as diffusion, cross-diffusion and self-diffusion, and drif...

This study examines the role of online social network proximity in cross-national diffusion of offline protests. Drawn upon Valente’s (1995) network diffusion model, the study operationalizes social network proximity-based protest exposure, using the international Facebook friendship share data. One year-long onsite protests during Arab Spring 2011 are examined using event history modeling. The...