In this paper, we obtain a finite-time non-blow-up result for the sub-Laplacian 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.
- Logarithmic Sobolev-Folland-Stein inequality
- stratified groups
ASJC Scopus subject areas
- Mathematics (miscellaneous)