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

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.

Automated summary

In this paper, we obtain finite-time non-blow-up and blow-up results for the sub-Laplacian heat equations with logarithmic nonlinearity on stratified groups. The logarithmic Sobolev-Folland-Stein inequality is crucial in our proof.