Wavefront Solutions for Reaction-diffusion-convection Models with Accumulation Term and Aggregative Movements

TL;DR

This paper investigates wavefront solutions of reaction-diffusion-convection PDEs with accumulation terms, allowing sign-changing diffusivity and accumulation functions, providing existence results, wave speed estimates, and classification of wave types.

Contribution

It introduces new existence results for traveling wave solutions in models with sign-changing diffusivity and accumulation functions, and classifies wavefront types.

Findings

Existence of traveling wave solutions under certain conditions.

Estimate of the threshold wave speed for solutions.

Classification of wavefronts into classical and sharp types.

Abstract

In this paper we analyze the wavefront solutions of parabolic partial differential equations of the type \[ g(u)u_{\tau}+f(u)u_{x}=\left(D(u)u_{x}\right)_{x}+\rho(u),\quad u\left(\tau,x\right)\in[0,1] \] where the reaction term $\rho$ is of monostable-type. We allow the diffusivity $D$ and the accumulation term $g$ to have a finite number of changes of sign. We provide an existence result of travelling wave solutions (t.w.s.) together with an estimate of the threshold wave speed. Finally, we classify the t.w.s. between classical and sharp ones.