Travelling Wave Solutions of Reaction-Diffusion Models with Density-Dependent 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...

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...

Self-similar solutions to a density-dependent reaction-diffusion model.

In this paper, we investigated a density-dependent reaction-diffusion equation, u(t)=(u(m))(xx)+u-u(m). This equation is known as the extension of the Fisher or Kolmogoroff-Petrovsky-Piscounoff equation, which is widely used in population dynamics, combustion theory, and plasma physics. By employing a suitable transformation, this equation was mapped to the anomalous diffusion equation where th...

Travelling Wave Solutions in Delayed Reaction Diffusion Systems with Partial Monotonicity

This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of “desirable pair of upper-lower solutions”, through which a subset can be constructed. We then apply the Schauder’s fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.