Linear and nonlinear heat equations on a $p$ -adic ball

• Date: 2018
• Main Authors: Kochubei, A. N., Кочубей, А. Н.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2018
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1550
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study the Vladimirov fractional differentiation operator $D^{\alpha}_N,\; \alpha > 0,\; N \in Z$, on a $p$-adic ball B$B_N = \{ x \in Q_p : | x|_p \leq p^N\}$. To its known interpretations via the restriction of a similar operator to $Q_p$ and via a certain stochastic process on $B_N$,...