A comparison principle for nonlinear heat Rockland operators on graded groups

TL;DR

This paper establishes a comparison principle for nonlinear heat Rockland operators on graded groups, providing a simple algebraic proof and applying it to demonstrate global boundedness of solutions for certain nonlinear heat equations on stratified groups.

Contribution

It introduces a new comparison principle for nonlinear heat Rockland operators with a straightforward algebraic proof and applies it to nonlinear heat equations on stratified groups.

Findings

Comparison principle for nonlinear heat Rockland operators established

Simple algebraic proof provided for the comparison principle

Global boundedness of solutions for nonlinear heat p-sub-Laplacian equations proved

Abstract

In this note we show a comparison principle for nonlinear heat Rockland operators on graded groups. We give a simple proof for it using purely algebraic relations. As an application of the established comparison principle we prove the global in $t$-boundedness of solutions for a class of nonlinear equations for the heat $p$-sub-Laplacian on stratified groups.