论文标题
较高维度的扩散变化二分法的临界长度
Critical length for the spreading-vanishing dichotomy in higher dimensions
论文作者
论文摘要
我们考虑了经典Fisher-Kolmogorov方程的扩展名，称为\ textit {Fisher-Stefan}模型，这是$ 0 <x <l（t）$的移动边界问题。 Fisher-Stefan模型的关键特性是\ textIt {蔓延 - 延伸二分法}，其中使用$ l（t）> l _ {\ textrm {c}} $的解决方案最终将以$ t \ to \ infty $传播，而解决方案则是$ l（t）\ ngtr l _ $ ngtr l _ $ _ { \ infty $。在一个维度上，众所周知，临界长度为$ l _ {\ textrm {c}}} =π/2 $。在这项工作中，我们将Fisher-Stefan模型重新构建在更高的维度上，并计算$ L _ {\ textrm {C}} $作为径向对称坐标系中空间维度的函数。我们的结果表明，$ l _ {\ textrm {c}} $如何取决于问题的维度和管理部分微分方程的数值解决方案与我们的计算一致。
We consider an extension of the classical Fisher-Kolmogorov equation, called the \textit{Fisher-Stefan} model, which is a moving boundary problem on $0 < x < L(t)$. A key property of the Fisher-Stefan model is the \textit{spreading-vanishing dichotomy}, where solutions with $L(t) > L_{\textrm{c}}$ will eventually spread as $t \to \infty$, whereas solutions where $L(t) \ngtr L_{\textrm{c}}$ will vanish as $t \to \infty$. In one dimension is it well-known that the critical length is $L_{\textrm{c}} = π/2$. In this work we re-formulate the Fisher-Stefan model in higher dimensions and calculate $L_{\textrm{c}}$ as a function of spatial dimensions in a radially symmetric coordinate system. Our results show how $L_{\textrm{c}}$ depends upon the dimension of the problem and numerical solutions of the governing partial differential equation are consistent with our calculations.
