Fish–hook shaped global bifurcation branch of a spatially heterogeneous cooperative system with cross-diffusion

Global Bifurcation for a Reaction-diffusion System with Inclusions

We consider a reaction-diffusion system exhibiting diffusion driven instability if supplemented by Dirichlet-Neumann boundary conditions. We impose unilateral conditions given by inclusions on this system and prove that global bifurcation of spatially nonhomogeneous stationary solutions occurs in the domain of parameters where bifurcation is excluded for the original mixed boundary value proble...

Spatially Varied Flow Profiles in a V-Shaped Side-Channel

Bifurcation analysis of a predator–prey system with self- and cross-diffusion and constant harvesting rate

In this paper, we focus on a ratio dependent predator–prey system with selfand cross-diffusion and constant harvesting rate. By making use of a brief stability and bifurcation analysis, we derive the symbolic conditions for Hopf, Turing and wave bifurcations of the system in a spatial domain. Additionally, we illustrate spatial pattern formations caused by these bifurcations via numerical examp...

Global Well-Posedness of a Conservative Relaxed Cross Diffusion System

We prove global existence in time of solutions to relaxed conservative cross diffusion systems governed by nonlinear operators of the form ui → ∂tui − ∆(ai(ũ)ui) where the ui, i = 1, ..., I represent I density-functions, ũ is a spatially regularized form of (u1, ..., uI) and the nonlinearities ai are merely assumed to be continuous and bounded from below. Existence of global weak solutions is o...

On Global Existence of Solutions to a Cross-diffusion System

the Laplacian, ∂/∂ν denotes the directional derivative along the outward normal on ∂Ω, ai, bi, ci, di (i = 1, 2) are given positive constants and α, γ, δ, β are nonnegative constants. In the system (1.1) u and v are non-negative functions which represent population densities of two competing species, d1 and d2 are respectively their diffusion rates. Parameters a1 and a2 are intrinsic growth rat...