A Heat Equation on some Adic Completions of Q and Ultrametric Analysis

2017/01/30 by Aguilar-Arteaga, Victor A., Cruz-López, Manuel, Arias, Samuel Estala
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1701.08732

Abstract

This article deals with a Markov process related to the fundamental solution of a heat equation on the direct product ring Q_S, where Q_S is a finite direct product of p-adic fields. The techniques developed here are different from the well known ones: they are geometrical and very simple. As a result, the techniques developed here provides a general framework of these problems on other related ultrametric groups.

Related

• Taibleson Operators, p-adic Parabolic Equations and Ultrametric Diffusion
• Linear and Nonlinear Heat Equations on a p-Adic Ball
• A non-autonomous p-Adic diffusion equation on time changing graphs
• Introduction to the p-adic Space
• Heat properties for groups