Travelling wave solutions of a Reaction-Diffusion System: Slow Reaction and Slow Diffusion

Travelling Wave Solutions of the One Dimensional Diffusion-reaction Equation

Existence of travelling wave solutions in delayed reaction–diffusion systems with applications to diffusion–competition systems

This paper is concerned with the existence of travelling wave solutions in a class of delayed reaction–diffusion systems without monotonicity, which concludes two-species diffusion–competition models with delays. Previous methods do not apply in solving these problems because the reaction terms do not satisfy either the so-called quasimonotonicity condition or non-quasimonotonicity condition. B...

The Evolution of Slow Dispersal Rates: a Reaction Diffusion Model

We consider n phenotypes of a species in a continuous but heterogeneous environment. It is assumed that the phenotypes diier only in their diiusion rates. With haploid genetics and a small rate of mutation, it is shown that the only nontrivial equilibrium is a population dominated by the slowest diiusing phenotype. We also prove that if there are only two possible phenotypes, then this equilibr...

Travelling waves in a reaction-diffusion system modelling fungal mycelia

We discuss travelling-wave solutions of a system of coupled reaction-diffusion equations used by the authors to describe the macroscopic behaviour of fungal mycelia. Such systems have been used in a multitude of applications; and, in particular, Merkin and Needham (1990, Proc. R. Soc. Lond. A 430, 315-45) have studied a certain formulation as a model for generic isothermal chemical reactions. W...

Exact Travelling Wave Solutions of Reaction-diffusion Models of Fractional Order∗

Abstract Reaction-diffusion models are used in different areas of chemistry problems. Also, coupled reaction-diffusion systems describing the spatiotemporal dynamics of competition models have been widely applied in many real world problems. In this paper, we consider a coupled fractional system with diffusion and competition terms in ecology, and reaction-diffusion growth model of fractional o...