Stability of travelling-wave solutions for reaction-diffusion-convection systems

Travelling Waves for Reaction-diffusion-convection Systems

(1) ut = Auxx + f(u), u ∈ R , x ∈ R, t ∈ [0,∞), where A is a real, positive-definite, N × N matrix and f : R → R is a continuously differentiable nonlinear function. The vector u may represent, for example, the concentrations of chemicals or the population densities of interacting species, the interactions between components of u being modelled by the reaction term f(u) and their diffusion by A...

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...

Travelling Wave for Absorption-convection-diffusion Equations

In this paper, we use the phase plane method for finding finite travelling waves solutions for the diffusion-absorption-convection equation ut = A(|ux|ux)x + B(u)x − Cu , (x, t) ∈ R× R. We show that the existence of solutions which depends on the parameters p, q and n. Also we study the asymptotic behavior of these solutions.

Travelling Wave Solutions of the One Dimensional Diffusion-reaction Equation

Travelling waves in nonlinear diffusion-convection-reaction

The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the study of a singular nonlinear integral equation. This article is devoted to demonstrating how this c...