Fujita exponent on stratified Lie groups

TL;DR

This paper establishes the Fujita exponent for semilinear heat equations on stratified Lie groups, extending Euclidean results and introducing new proof techniques specific to nilpotent Lie groups.

Contribution

It proves that the critical Fujita exponent is Q/(Q-2) for stratified Lie groups, generalizing Euclidean results and providing new methods for analysis on nilpotent Lie groups.

Findings

Fujita exponent is Q/(Q-2) for stratified Lie groups

Extension of Euclidean results to nilpotent Lie groups

Introduction of new proof techniques involving test functions and fixed point theorem

Abstract

We prove that $\frac{Q}{Q-2}$ is the Fujita exponent for a semilinear heat equation on an arbitrary stratified Lie group with homogeneous dimension $Q$. This covers the Euclidean case and gives new insight into proof techniques on nilpotent Lie groups. The equation we study has a forcing term which depends only upon a group element and has positive integral. The stratified Lie group structure plays an important role in our proofs, along with test function method and Banach fixed point theorem.