论文标题
Bramson在拉的前部和推动前部的过渡时的跨越
Cross-overs of Bramson's shift at the transition between pulled and pushed fronts
论文作者
论文摘要
拉动前部位置的Bramson对数偏移是一大类一类可承受的波动波方程共有的通用特征。随着一种非线性的变化，碰巧的是，人们可以在某种临界的非线性性下观察到从拉的前部到推动的前部的过渡。在此过渡时，Bramson Shift进行了修改。在时间到达无限且非线性变得至关重要的极限中，前部的位置表现出跨界。本注释的目的是给出该交叉函数的表达，该函数是一个完全可溶的模型，希望该表达式在拉动前部和推动前部之间的过渡时对更通用的波动波方程保持有效。对于此特定模型，还获得了其他跨界功能，以描述对初始条件或截止效果的依赖性。
The Bramson logarithmic shift of the position of pulled fronts is a universal feature common to a large class of monostable traveling wave equations. As one varies the non-linearities it so happens that one can observe, at some critical non linearity, a transition from pulled fronts to pushed fronts. At this transition the Bramson shift is modified. In the limit where time goes to infinity and the non-linearity becomes critical, the position of the front exhibits a cross-over. The goal of the present note is to give the expression of this cross-over function, for a particular model which is exactly soluble, with the hope that this expression would remain valid for more general traveling wave equations at the transition between pulled and pushed fronts. Other cross-over functions are also obtained, for this particular model, to describe the dependence on initial conditions or the effect of a cut-off.
