发表机构
School of Mathematical Sciences, South China Normal University; School of Mathematical Sciences and Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China（华南师范大学数学科学学院; 中国科学技术大学数学科学学院与吴文俊数学重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对带周期平流项的反应-扩散方程，构造双稳脉动波并证明其收敛于均匀化波，推导速度展开式，揭示平流非均匀性可加速或减速传播。
AI 中文摘要
我们研究任意空间维度中具有一般周期平流项的反应-扩散方程的双稳脉动波，允许扩散矩阵非对称。假设均匀化方程在给定方向上存在非零速度的行波，我们为所有足够小的空间周期$L$构造移动脉动波，并证明当$L\ o0^+$时它们收敛到均匀化波。当均匀化速度从不消失时，存在范围和收敛性在传播方向上是一致的。我们还证明了任意周期下波速的唯一性、移动波的剖面唯一性，以及在竞争剖面连续性条件下驻波情形下静止波的唯一性。对于空间齐次反应，我们推导出展开式$c_L=c_0+Lc_1+O(L^2)$以及$c_1$的显式公式。具有常数扩散和零均值周期平流项的示例表明，$c_1$可以取正或负号，这证明平流项中的非均匀性可能相对于均匀化极限加速或减速传播，并且一般的$O(L)$速度估计是尖锐的。
英文摘要
We study bistable pulsating waves for reaction-diffusion equations with general periodic advection in arbitrary space dimension, allowing the diffusion matrix to be nonsymmetric. Assuming that the homogenized equation admits a traveling wave with nonzero speed in a given direction, we construct moving pulsating waves for all sufficiently small spatial periods $L$ and prove their convergence to the homogenized wave as $L\to0^+$. The existence range and convergence are uniform in the propagation direction when the homogenized speeds never vanish. We also prove uniqueness of the wave speed for arbitrary periods, profile uniqueness for moving waves, and stationary-wave uniqueness in the standing case under continuity of the competing profile. For spatially homogeneous reactions, we derive the expansion $c_L=c_0+Lc_1+O(L^2)$ and an explicit formula for $c_1$. Examples with constant diffusion and zero-mean periodic advection show that $c_1$ can have either sign, demonstrating that the heterogeneity in advection may accelerate or decelerate propagation relative to the homogenized limit and that the general $O(L)$ speed estimate is sharp.
