Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system the presence of spatial heterogeneity both transport reaction terms. Under suitable asymptotic assumption that is slow over domain, while gradients are not too sharp, stability steady state approximated absence transport. U...

Abstract Our concern in this paper is to shed some additional light on the mechanism and effect caused by so called cross-diffusion. We consider a two-species reaction–diffusion (RD) system. Both “fluxes” contain gradients of both unknown solutions. show that–for parameter range– there exist two different type periodic stationary Using them, we are able divide into parts (eight-dimensional) spa...