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We consider some cross diffusion systems which is inspired by models in mathematical biology/ecology, in particular the Shigesada-Kawasaki-Teramoto (SKT) model in population biology. We establish the global existence of strong solutions to…
In this article we study a reaction diffusion system with $m$ unknown concentration. The non-linearity in our study comes from an underlying reversible chemical reaction and triangular in nature. Our objective is to understand the large…
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…
We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…
We study a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions. Our system models a competition relationship that one species escape from the region of high population density of their competitors in…
Starting from the dynamical system model capturing the splitting-differentiation process of populations, we extend this notion to show how the speciation mechanism from a single species leads to the consideration of several well known…
Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type…
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…
In this article we introduce an original model in order to study the emergence of chaos in a reaction diffusion system in the presence of self- and cross-diffusion terms. A Fourier Spectral Method is derived to approximate equilibria and…
A general class of cross-diffusion systems for two population species in a bounded domain with no-flux boundary conditions and Lotka-Volterra-type source terms is analyzed. Although the diffusion coefficients are assumed to depend linearly…
This paper deals with the existence of global weak solutions for a wide class of (multiple species) cross-diffusions systems. The existence is based on two different ingredients: an entropy estimate giving some gradient control and a…
We study analytically and numerically a bistable reaction-diffusion equation on an arbitrary finite network. We prove that stable fixed points (multi-fronts) exist for any configuration as long as the diffusion is small. We also study fold…
In this note we present a study of the solutions associated to a particular spatial extension of the Rosenzweig-MacArthur model for predator and prey. The analysis presented here shows that positive steady state solutions emerge via a…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
This paper concerns pattern formation in a class of reaction-advection-diffusion systems modeling the population dynamics of two predators and one prey. We consider the biological situation that both predators forage along the population…
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…
The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. Such problems describe biological processes and chemical reactions in which diffusive and…
We study reaction-diffusion processes with concentration-dependent diffusivity. First, we determine the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes. We then consider two…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…
We prove that the steady state of a class of multidimensional reaction-diffusion systems is asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, and pay particular attention to a special…