Related papers: On the influence of cross-diffusion in pattern for…
In this paper we analyse a finite volume scheme for a nonlocal version of the Shigesada-Kawazaki-Teramoto (SKT) cross-diffusion system. We prove the existence of solutions to the scheme, derive qualitative properties of the solutions and…
We prove the existence and uniqueness of solution of a nonlocal cross-diffusion competitive population model for two species. The model may be considered as a version, or even an approximation, of the paradigmatic…
We establish the uniqueness and regularity of weak (and very weak) solutions to a class of cross diffusion systems which is inspired by models in mathematical biology/ecology, in particular the Shigesada-Kawasaki-Teramoto (SKT) model in…
A class of hyperbolic reaction--diffusion models with cross-diffusion is derived within the context of Extended Thermodynamics. Linear stability analysis is performed to study the nature of the equilibrium states against uniform and…
Some quantities in the reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead of local density functions. We show that such nonlocal spatial average can induce instability of…
A self-consistent equation to derive a discreteness-induced stochastic steady state is presented for reaction-diffusion systems. For this formalism, we use the so-called Kuramoto length, a typical distance over which a molecule diffuses in…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
The global existence of classical solutions to cross diffusion systems of more than 2 equations given on a planar domain is established. The results can apply to generalized Shigesada-Kawasaki-Teramoto (SKT) and food pyramid models whose…
This paper deals with the stability analysis for steady-states perturbed by the full cross-diffusion limit of the SKT model with Dirichlet boundary conditions. Our previous result showed that positive steady-states consist of the branch of…
The existence of global-in-time weak solutions to reaction-cross-diffusion systems for an arbitrary number of competing population species is proved. The equations can be derived from an on-lattice random-walk model with general transition…
In this paper,under an abstract setting we establish the existence of spatially inhomogeneous steady states and the asymptotic propagation properties for a large class of monotone evolution systems without spatial translation invariance.…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
The concept of cross diffusion is applied to some biological systems. The conditions for persistence and Turing instability in the presence of cross diffusion are derived. Many examples including: predator-prey, epidemics (with and without…
An implicit Euler finite-volume scheme for an $n$-species population cross-diffusion system of Shigesada--Kawasaki--Teramoto-type in a bounded domain with no-flux boundary conditions is proposed and analyzed. The scheme preserves the formal…
This paper is concerned with existence, non-existence and uniqueness of positive (coexistence) steady states to a predator-prey system with density-dependent dispersal. To overcome the analytical obstacle caused by the cross-diffusion…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
In this paper we investigate pattern formation in Keller--Segel chemotaxis models over a multi--dimensional bounded domain subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its…
In this study, a spatially distributed reaction-diffusion-advection (RDA) model with harvesting is investigated to signify the outcome of a competition between two competing species in a heterogeneous environment. The study builds upon the…
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…
In this work we use functional methods to prove the boundedness and global existence of solutions for a class of strongly coupled parabolic systems. We apply the results to deduce the global existence of solutions for a classic…