论文标题
完全非局部热方程的大型行为
Large-time behavior for a fully nonlocal heat equation
论文作者
论文摘要
我们研究所有$ l^p $规范中的大型行为以及在$ \ mathbb {r}^n $中涉及caputo $α$α$ - 时间的衍生物和laplacian $（ - δ）^s $，$ s \ in（0,11）$的$ suffere的$（$ s）$的$ \ mathbb {r}^n $的不同时空解决方案中的大型行为。假定初始数据是可以集成的，并且在需要时也可以在$ l^p $中。关于案例的主要新颖性$ s = 1 $来自快速尺度的行为，由于方程式的基本解决方案的胖尾巴，我们能够给出的结果既不可用于$ s = 1 $也不可用于标准热量方程式，$ s = 1 $，$ s = 1 $，$ a $α= 1 $。
We study the large-time behavior in all $L^p$ norms and in different space-time scales of solutions to a nonlocal heat equation in $\mathbb{R}^N$ involving a Caputo $α$-time derivative and a power of the Laplacian $(-Δ)^s$, $s\in (0,1)$, extending recent results by the authors for the case $s=1$. The initial data are assumed to be integrable, and, when required, to be also in $L^p$. The main novelty with respect to the case $s=1$ comes from the behaviour in fast scales, for which, thanks to the fat tails of the fundamental solution of the equation, we are able to give results that are not available neither for the case $s=1$ nor, to our knowledge, for the standard heat equation, $s=1$, $α=1$.
