p-Adic球上的线性和非线性Heat Equations
Linear and Nonlinear Heat Equations on a p-Adic Ball
摘要：
研究了$p$ -adic球$B_N=\{ x\in \mathbb Q_p:\ |x|_p\le p^N\}$上的Vladimirov分数阶微分算子$D^α_N$，$α>0, N\in \mathbb Z$.通过限制从一个类似的运营商在$\mathbb Q_p$和通过一定的随机过程在$B_N$上的已知的解释，我们添加了一个解释作为一个伪微分算子在添加剂组的$B_N$的庞特里亚金对偶。本文研究了$D^α_N$的格林函数和$B_N$上的一个非线性方程，该方程类似于经典的多孔介质方程.
英文摘要：
We study the Vladimirov fractional differentiation operator $D^α_N$, $α>0, N\in \mathbb Z$, on a $p$-adic ball $B_N=\{ x\in \mathbb Q_p:\ |x|_p\le p^N\}$. To its known interpretations via restriction from a similar operator on $\mathbb Q_p$ and via a certain stochastic process on $B_N$, we add an interpretation as a pseudo-differential operator in terms of the Pontryagin duality on the additive group of $B_N$. We investigate the Green function of $D^α_N$ and a nonlinear equation on $B_N$, an analog the classical porous medium equation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
