Bramson的转变在拉和推前线之间的过渡处的交叉
Cross-overs of Bramson's shift at the transition between pulled and pushed fronts
摘要：
拉阵面位置的Bramson对数移动是一个普遍的特征，是一大类单稳态行波方程的共同点。当人们改变非线性时，在某个临界非线性处，人们可以观察到从拉前沿到推前沿的过渡。在这个转变中，Bramson移位被修改。在时间趋于无穷大且非线性变得临界的极限中，前沿的位置表现出交叉。本说明的目的是给出这个交叉函数的表达式，对于一个特定的模型，这是完全可解的，希望这个表达式将保持有效的更一般的行波方程之间的过渡拉和推前。对于这个特定的模型，还获得了其他交叉函数，以描述对初始条件的依赖性或截止效应。
英文摘要：
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.
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