论文标题
在时间周期转移环境中反应扩散方程的传播动力学
Propagation dynamics of a reaction-diffusion equation in a time-periodic shifting environment
论文作者
论文摘要
本文涉及非自主反应 - 扩散方程\ [u_t = u_ {xx}+ug（t，x-ct，u），\ quad t> 0，x \ in \ mathbb {r}，\]，$ c \ in $ c \ in \ mathbb {r} $ in \ mathb {r} $ shift the shiftting speed nontione $ ugtity $ ug ugtie $ ugtie $ ugtie $ ug ug KPP类型渐近为$ξ\ to- \ infty $，为$ξ\ to+\ infty $。在下均匀性的条件下，我们表明存在$ c^*> 0 $，因此如果并且仅$ | c | <c^*$存在唯一的强制时间周期浪潮，并且它根据初始值的尾部行为在某些意义上吸引了其他解决方案。在$ | c | \ ge c^*$的情况下，传播动力学类似于限制系统的$ξ\ to \ pm \ infty $，具体取决于转移方向。
This paper concerns the nonautonomous reaction-diffusion equation \[ u_t=u_{xx}+ug(t,x-ct,u), \quad t>0,x\in\mathbb{R}, \] where $c\in\mathbb{R}$ is the shifting speed, and the time periodic nonlinearity $ug(t,ξ,u)$ is asymptotically of KPP type as $ξ\to-\infty$ and is negative as $ξ\to+\infty$. Under a subhomogeneity condition, we show that there is $c^*>0$ such that a unique forced time periodic wave exists if and only $|c|< c^*$ and it attracts other solutions in a certain sense according to the tail behavior of initial values. In the case where $|c|\ge c^*$, the propagation dynamics resembles that of the limiting system as $ξ\to\pm \infty$, depending on the shifting direction.
