Non-blow-up and blow-up results to heat equations with logarithmic nonlinearity on stratified groups

Abstract

In this paper, we obtain a finite-time non-blow-up result for the subLaplacian heat equations with logarithmic nonlinearity on stratified groups. In our proof, the logarithmic Sobolev-Folland-Stein inequality plays a key role. We also establish a blow-up result at infinite time  on stratified groups.