A NONAUTONOMOUS p-ADIC DIFFUSION EQUATION ON TIME CHANGING GRAPHS

Abstract

Motivated by the recently proven presence of ultrametricity in physical models (certain spin glasses), the very recent study of Turing patterns on locally ultrametric state spaces, and the study of Turing patterns in time changing networks, first nonautonomous diffusion operators on such systems, where finitely many compact p-adic spaces are joined by a graph structure, are studied, including their Dirichlet and von Neumann eigenvalues. Secondly, the Cauchy problem for the heat equation associated with these operators is solved, its solution approximated by Trotter products, and thirdly, the corresponding Feller property as well as the Markov property (a Hunt process) is established.