Cross-diffusion phenomena are experimentally shown to be able to induce convective fingering around an initially stable stratification of two microemulsions with different compositions. Upon diffusion of a salt that entrains water and AOT micelles by cross-diffusion, the miscible interface deforms into fingers following the build-up of a non-monotonic density profile in the gravitational field....

The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion system with cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with...

Please cite this article in press as: M. Frittelli, et al., Lumped finite elements for reaction–cross-diffusion systems on stationary surfaces, Computers and Mathematics with Applications (2017), http://dx.doi.org/10.1016/j.camwa.2017.07.044. 2 M. Frittelli et al. / Computers and Mathematics with Applications ( ) – the concept of cross-diffusion includes well-known processes such as chemoand ha...

This paper is concerned with a diffusive prey-predator model with modified Leslie-Gower term and Holling II functional response subject to the homogeneous Neumann boundary condition. Firstly, by upper and lower solutions method, we prove the global asymptotic stability of the unique positive constant steady state solution. Secondly, introducing the cross diffusion, we obtain the existence of no...

Keywords: Predator–prey model Stage-structure Stability Cross-diffusion Non-constant positive steady states a b s t r a c t This paper is concerned with the reaction diffusion version with homogeneous Neumann boundary conditions of a stage-structured predator–prey model. We first show that the nonnegative constant steady states are globally stable, which implies that corresponding elliptic syst...

Cross-diffusion driven instabilities have gained a considerable attention in the field of population dynamics, mainly due to their ability to predict some important features in the study of the spatial distribution of species in ecological systems. This paper is concerned with some mathematical and numerical aspects of a particular reaction–diffusion system with cross-diffusion, modeling the ef...

In this paper, we consider the effect of time delay and cross diffusion on the dynamics of a predator-prey model with the Allee effect. We mainly investigate the stability of the homogeneous state points and give the conditions of time delay and cross diffusion driven instability in details. Furthermore, we illustrate the spatial patterns via numerical simulations, which show that the model dyn...