A comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups

TL;DR

This paper establishes a comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups, leading to blow-up results and boundedness of solutions, extending previous work in the field.

Contribution

It introduces a new comparison principle for complex operators on graded Lie groups, generalizing prior results and enabling analysis of solution behavior.

Findings

Established a comparison principle for nonlinear hypoelliptic heat operators.

Derived blow-up and boundedness results for solutions of nonlinear heat equations.

Extended previous results to more general graded Lie group settings.

Abstract

In this paper we present a comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups. Moreover, using the comparison principle we obtain blow-up type results and global in $t$-boundedness of solutions of nonlinear equations for the heat $p$-sub-Laplacian on stratified Lie groups. In particular, this paper generalises and extends previous results obtained by the first author and Suragan in [RS18].