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

  • A. N. Kochubei

Abstract

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.
Published
25.02.2018
How to Cite
KochubeiA. N. “Linear and Nonlinear Heat Equations on a $p$ -Adic Ball”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 2, Feb. 2018, pp. 193-05, http://umj.imath.kiev.ua/index.php/umj/article/view/1550.
Section
Research articles