论文标题
离散反应扩散方程的行驶波的速度图
Velocity diagram of traveling waves for discrete reaction-diffusion equations
论文作者
论文摘要
我们考虑反应扩散方程的离散版本。一个典型的例子是完全阻尼的Frenkel-Kontorova模型，其中速度与力成正比。我们还引入了$σ$表示的额外外部力。对于一般离散和完全非线性动力学，我们根据参数$σ$研究速度$ c = c（σ）$的行进波。在某些假设下，我们显示了$ c（σ）$ for $σ\ in [σ^ - ，σ^+] $的属性。我们表明，速度$ c $在$σ\ in（σ^ - ，σ^+）$中的$ c $在BISCABLECIME中的$中，垂直分支$ C \ ge C^+$ for $σ=σ^+$和$ C \ le c \ le c \ le c \ le c^ - $ c^$ for $ c^$ for $ c = for $σ=σ=σ^ - $ in Monostable in of Monostable in of Monostable in nonostable in nonostable in nonostable in nonostable in in sonostable crime in。
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 $σ\in [σ^-,σ^+]$. We show that the velocity $c$ is nondecreasing in $σ\in (σ^-,σ^+)$ in the bistable regime, with vertical branches $c\ge c^+$ for $σ=σ^+$ and $c\le c^-$ for $σ=σ^-$ in the monostable regime.
