Nonexistence results for a semilinear heat equation with Hardy potential on stratified Lie groups

Durvudkhan Suragan, Bharat Talwar

Published 2023-11-18Version 1

A simple explanation is provided to explain why weighted blow up is observed for weak solutions of certain semilinear heat equations with Hardy potential. The problem we study has a power non-linearity and a forcing term which depends only upon the space variable. Local and global nonexistence results are provided for this problem. In addition, local existence is proved when the gradient term appearing in the Hardy potential is unimodular almost everywhere. Under additional assumption that the forcing term depends on time as well, global existence is also proved. Through these existence results we predict the critical exponents for the existence of local and global solutions.