Related papers: Well-posedness of a cross-diffusion population mod…

This paper is concerned with a diffusive predator-prey model with predator-taxis and prey-taxis. Based on the Schauder fixed point theorem, we prove the global existence, uniqueness and boundedness of the classical solutions under the…

We are concerned with the persistence of both predator and prey in a diffusive predator-prey system with a climate change effect, which is modeled by a spatial-temporal heterogeneity depending on a moving variable. Moreover, we consider…

We rigorously prove the passage from a Lotka-Volterra reaction-diffusion system towards a cross-diffusion system at the fast reaction limit. The system models a competition of two species, where one species has a more diverse diet than the…

This paper is concerned with two frequency-dependent SIS epidemic reaction-diffusion models in heterogeneous environment, with a cross-diffusion term modeling the effect that susceptible individuals tend to move away from higher…

We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the…

In this article we prove local-in-time existence and uniqueness of solution to a non-isothermal cross-diffusion system with Maxwell-Stefan structure.

We discuss the existence of stationary solutions for logistic diffusion equations of Fisher-Kolmogoroff-Petrovski-Piskunov type driven by the superposition of fractional operators in a bounded region with "hostile" environmental conditions,…

We study a generalization of a cross-diffusion problem deduced from a nonlinear complex-variable diffusion model for signal and image denoising. We prove the existence of weak solutions of the time-independent problem with fidelity terms…

Consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources distribution in a given box. We…

We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a linear pressure law and different mobilities. For arbitrary bounded non-negative initial data, we show that any good approximation…

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…

In this paper, we study the global dynamics of a general $2\times 2$ competition models with nonsymmetric nonlocal dispersal operators. Our results indicate that local stability implies global stability provided that one of the diffusion…

We study quasilinear reaction diffusion systems relative to the Shigesada-Kawasaki-Teramoto model. Nonlinearity standing for the external force is provided with mass dissipation. Estimate in several norms of the solution is provided under…

Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…

The Kimura equation is a degenerated partial differential equation of drift-diffusion type used in population genetics. Its solution is required to satisfy not only the equation but a series of conservation laws formulated as integral…

This paper is concerned with the classical two-species Lotka-Volterra diffusion system with strong competition. The sharp dynamical behavior of the solution is established in two different situations: either one species is an invasive one…

For cross-diffusion systems possessing an entropy (i.e. a Lyapunov functional)we study nonlocal versions and exhibit sufficient conditions to ensure that thenonlocal version inherits the entropy structure. These nonlocal systems can…

It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an…

We investigate the existence and instability of a class of blowing-up positive steady states arising in a shadow system of the Shigesada-Kawasaki-Teramoto (SKT) two-species competition model, as well as in the corresponding perturbed SKT…

In this paper we present and analyse a simple two populations model with migrations among two different environments. The populations interact by competing for resources. Equilibria are investigated. A proof for the boundedness of the…