Recently reaction–diffusion approximation has been intensively studied. This paper reviews
the studies in reaction–diffusion approximation and is based on Iida and Ninomiya (Sugaku …

The purpose of this chapter is to investigate the singular limit of reaction-diffusion systems
or, more precisely, the fast reaction limit of competition-diffusion systems. It often turns out …

Our interest here is to find the invader in a two species, diffusive and competitive Lotka–
Volterra system in the particular case of travelling wave solutions. We investigate the role of …

We study the numerical approximation of the solutions of a class of nonlinear reaction–
diffusion systems modelling predator–prey interactions, where the local growth of prey is …

We discuss some recent results on symmetry of solutions of nonlinear partial differential
equations. We focus on elliptic and degenerate elliptic boundary value problems of second …

We consider a coupled bulk-surface system of partial differential equations with nonlinear
coupling modeling receptor-ligand dynamics. The model arises as a simplification of a …

We show that the Neumann boundary condition appears along the boundary of an inner
domain when the diffusivity of the outer domain goes to zero. We take Fick's diffusion law …

This paper analyzes the dynamics of a superlinear indefinite parabolic system. As a
byproduct, a number of new results related to population dynamics and economy are …

In this work, we discuss a cell–cell repulsion model based on a hyperbolic Keller–Segel
equation with two populations, which aims at describing the cell growth and dispersion in …

During the last 30 years, mathematical models have progressively earned their recognition
in the field of ecology. Though still not as used and trusted as in other scientific fields (Sagoff …