发表机构
South China Normal University; University of Science and Technology of China; Anhui University of Science and Technology（华南师范大学; 中国科学技术大学; 安徽理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究强剪切流中双稳行波的极限行为，证明速度归一化收敛及剖面子序列收敛，并构造例子表明零均值剪切可产生负、零或正极限速度，甚至反转传播方向。
AI 中文摘要
我们研究在具有周期横向边界条件的无限圆柱体中，双稳行波的强剪切极限。我们证明，对于每个足够正则的周期剪切剖面，当振幅趋于无穷大时，由流动振幅归一化的波前速度收敛。在适当的纵向重缩放和平移之后，相应的剖面沿子序列收敛到极限退化方程的完整波前。此外，在剪切的Hörmander型非退化条件下，极限波前被证明是正则的且在平移意义下唯一，并且整个归一化族一致收敛。一个主要困难在于，变号双稳反应允许极限过渡通过中间横向平衡态分裂。我们通过利用这些平衡态的不稳定性以及适当的正则化和比较论证来排除这种可能性。最后，与燃烧情形（其中每个非恒定零均值剪切产生正极限速度）形成对比，我们构造了一个例子表明，对于固定的双稳反应，光滑的零均值剪切可以产生负、零或正的极限速度。特别地，该例子表明，在小振幅下加速传播的剪切，当其振幅变大时可能反转传播方向。
英文摘要
We study the strong-shear limit of bistable traveling fronts in infinite cylinders with periodic transverse boundary conditions. We prove that, for every sufficiently regular periodic shear profile, the front speed normalized by the flow amplitude converges as the amplitude tends to infinity. After suitable longitudinal rescaling and translations, the corresponding profiles converge along subsequences to full fronts of the limiting degenerate equation. Furthermore, under a Hörmander-type non-degeneracy condition on the shear, the limiting front is proved to be regular and unique up to translation, and the whole normalized family converges uniformly. A main difficulty is that the sign-changing bistable reaction allows the limiting transition to split through intermediate transverse equilibria. We rule out this possibility by exploiting the instability of such equilibria together with suitable regularization and comparison arguments. Finally, in contrast with the combustion case, where every nonconstant mean-zero shear yields a positive limiting speed, we construct an example showing that, for a fixed bistable reaction, smooth mean-zero shears can produce negative, zero, or positive limiting speeds. In particular, the example shows that a shear which accelerates propagation at small amplitudes may reverse the propagation direction when its amplitude becomes large.
