@article{Kochubei_2018, title={Linear and nonlinear heat equations on a $p$ -adic ball}, volume={70}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/1550}, abstractNote={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 $B_N$, we add an interpretation as a pseudodifferential operator in terms of the Pontryagin duality on the additive group
of $B_N$. We investigate the Green function of $D^{\alpha}_N$ and a nonlinear equation on $B_N$, an analog of the classical equation of
porous medium.}, number={2}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={KochubeiA. N.}, year={2018}, month={Feb.}, pages={193-205} }