论文标题
在非本地线性化的Fisher-kpp方程中的大偏差和对数延迟的出现
Large deviations and the emergence of a logarithmic delay in a nonlocal linearised Fisher-KPP equation
论文作者
论文摘要
我们研究了通过非局部扩散的Fisher-KPP方程的变体。使用大偏差的理论，我们显示了带有阶梯式初始数据的线性化方程的“ bramson样”对数延迟的出现。我们得出的结论是，对于非线性方程的解决方案也出现了对数延迟。先前的论文发现了非线性方程非常精确的结果，对内核衰减的假设有很强的假设。我们的结果不那么精确，但是它们对于所有连续的对称薄尾核有效。
We study a variant of the Fisher-KPP equation with nonlocal dispersal. Using the theory of large deviations, we show the emergence of a "Bramson-like" logarithmic delay for the linearised equation with step-like initial data. We conclude that the logarithmic delay emerges also for the solutions of the nonlinear equation. Previous papers found very precise results for the nonlinear equation with strong assumptions on the decay of the kernel. Our results are less precise, but they are valid for all continuous symmetric thin-tailed kernels.
