空间周期格点Fisher--KPP方程的对数上界与轴向前沿选择
Logarithmic upper bounds and axial front selection for spatially periodic lattice Fisher--KPP equations
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中文总结 AI 辅助
针对空间周期格点Fisher--KPP方程，利用周期谱几何和热核方法，建立了入侵前沿的对数上界与轴向Bramson修正，并确定了临界脉动前沿的渐近形态。
中文摘要 AI 辅助
我们研究了高维格点上空间周期Fisher--KPP方程的入侵前沿的位置与形状，初始数据为局部化数据。周期谱几何决定了一个方向性的对数上界。当线性增长率不依赖于传播坐标时，我们证明了匹配的轴向Bramson修正，并确定了解所趋近的临界脉动前沿。所选轮廓包含局部周期胞腔和一个导数趋于零的有界相位。该描述还确定了规定水平到达远处格点的时间以及水平或相邻胞腔之间的渐近时间间隔。证明结合了周期横向热核、标量下比较和临界尾部分析。对于每个坐标都变化的增长率，正Dirichlet商比较将匹配下界简化为对线性种子及其累积非线性损失的两个显式估计。
英文摘要
We study the position and shape of invasion fronts for spatially periodic Fisher--KPP equations on higher-dimensional lattices, starting from localized initial data. Periodic spectral geometry determines a directional logarithmic upper bound. When the linear growth rate is independent of the propagation coordinate, we prove the matching axial Bramson correction and identify the critical pulsating front approached by the solution. The selected profile includes the local periodic cell and a bounded phase whose derivative tends to zero. This description also determines the times at which prescribed levels reach distant lattice sites and the asymptotic time gaps between levels or neighboring cells. The proof combines a periodic transverse heat kernel, a scalar lower comparison, and critical-tail analysis. For growth rates varying in every coordinate, a positive Dirichlet quotient comparison reduces the matching lower bound to two explicit estimates on the linear seed and its accumulated nonlinear loss.
