# Evolution problems with perturbed 1-Laplacian type operators on random walk spaces

## TL;DR

This paper studies evolution problems involving perturbed 1-Laplacian type operators on random walk spaces, which generalize both graphs and nonlocal settings.

## Contribution

The novelty lies in analyzing functionals with different growth on multiple random walk structures or partitions.

## Key findings

- Evolution problems with different growth functionals on two random walk structures are studied.
- The paper addresses the case where functionals have different growth on a partition of the random walk space.
- Results contribute to understanding PDEs in nonlocal and graph-based settings.

## Abstract

Random walk spaces are a general framework for the study of PDEs. They include as particular cases locally finite weighted connected graphs and nonlocal settings involving symmetric integrable kernels on \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${\mathbb {R}}^N$$\end{document}RN. We are interested in the study of evolution problems involving two random walk structures so that the associated functionals have different growth on each structure. We also deal with the case of a functional with different growth on a partition of the random walk.