Velocity diagram of traveling waves for discrete reaction-diffusion equations

2022/09/10 by Haj, M. Al, Monneau, R.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.04637

Abstract

We consider a discrete version of reaction-diffusion equations. A typical example is the fully overdamped Frenkel-Kontorova model, where the velocity is proportional to the force. We also introduce an additional exterior force denoted by σ. For general discrete and fully nonlinear dynamics, we study traveling waves of velocity c=c(σ) depending on the parameter σ. Under certain assumptions, we show properties of the velocity diagram c(σ) for σ∈ [σ^-,σ⁺]. We show that the velocity c is nondecreasing in σ∈ (σ^-,σ⁺) in the bistable regime, with vertical branches c≥ c⁺ for σ=σ⁺ and c≤ c^- for σ=σ^- in the monostable regime.

Related

• Traveling waves for discrete reaction-diffusion equations in the general monostable case
• Traveling Waves in Bistable Reaction-Diffusion Cellular Automata
• Depinning transitions in discrete reaction-diffusion equations
• Travelling waves in a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypical trait
• Minimal Travelling Wave Speed and Explicit Solutions in Monostable Reaction-Diffusion Equations