Heat equation with a general stochastic measure on nested fractals

TL;DR

This paper studies a stochastic heat equation on nested fractals driven by a general stochastic measure, establishing conditions for the existence, uniqueness, and continuity of solutions when the spectral dimension is below 4/3.

Contribution

It introduces a framework for analyzing stochastic heat equations on nested fractals with general stochastic measures, extending previous results to broader fractal structures.

Findings

Existence and uniqueness of solutions are proven for spectral dimension < 4/3.

Solutions are shown to be continuous under specified conditions.

The approach broadens understanding of stochastic PDEs on fractal geometries.

Abstract

A stochastic heat equation on an unbounded nested fractal driven by a general stochastic measure is investigated. Existence, uniqueness and continuity of the mild solution are proved provided that the spectral dimension of the fractal is less than 4/3.