Linear and Nonlinear Heat Equations on a p-Adic Ball

2017/08/09 by Kochubei, Anatoly N. · 4 citations
#35K55 #35R11 (Secondary) #35S05 (Primary) 11S80 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1708.03261

Abstract

We study the Vladimirov fractional differentiation operator D^α_N, α>0, N∈ \mathbb Z, on a p-adic ball B_N=\ x∈ \mathbb Q_p: |x|_p≤ 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.

Cited by

• Hearing the Serre invariant of a compact p-adic analytic manifold
• Diffusion operators on p-adic analytic manifolds
• Geometry-induced criticality in p-adic scaling limits of random walks
• Non-Archimedean Neumann problem: weak and strong solutions

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