TY - JOUR
AU - A. N. Kochubei
PY - 2018/02/25
Y2 - 2020/11/27
TI - Linear and nonlinear heat equations on a $p$ -adic ball
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 70
IS - 2
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1550
AB - 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 processon $B_N$, we add an interpretation as a pseudodifferential operator in terms of the Pontryagin duality on the additive groupof $B_N$. We investigate the Green function of $D^{\alpha}_N$ and a nonlinear equation on $B_N$, an analog of the classical equation ofporous medium.
ER -