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Fujita exponent on stratified Lie groups

Durvudkhan Suragan, Bharat Talwar

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.

Fujita exponent on stratified Lie groups

Abstract

We prove that is the Fujita exponent for a semilinear heat equation on an arbitrary stratified Lie group with homogeneous dimension . 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.
Paper Structure (3 sections, 82 equations)

This paper contains 3 sections, 82 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Fujita exponent is $\frac{Q}{Q-2}$

Theorems & Definitions (6)

  • proof
  • proof
  • proof
  • proof
  • proof
  • proof