论文标题
从非线性热方程式从异常到经典扩散
From anomalous to classical diffusion in a non-linear heat equation
论文作者
论文摘要
在本文中，我们考虑了具有天然多项式非线性项的热方程。并在扩散项中有两种不同的情况。第一种情况（异常扩散）涉及参数$ 1 <α<2 $的分数拉普拉斯运算符，而第二种情况（经典扩散）涉及经典的拉普拉斯运算符。当$α\至2 $时，我们证明了异常扩散情况的溶液均匀收敛到经典扩散情况的溶液。此外，我们严格得出了收敛速率，这在以前的相关工作中是实验性的。
In this paper, we consider the heat equation with the natural polynomial non-linear term; and with two different cases in the diffusion term. The first case (anomalous diffusion) concerns the fractional Laplacian operator with parameter $1<α<2$, while, the second case (classical diffusion) involves the classical Laplacian operator. When $α\to 2$, we prove the uniform convergence of the solutions of the anomalous diffusion case to a solution of the classical diffusion case. Moreover, we rigorous derive a convergence rate, which was experimentally exhibit in previous related works.
