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

Kashkynbayev A. Kassymov A. Suragan D.
2023 Taylor and Francis Ltd.

Quaestiones Mathematicae
2023 #46 Issue 6 1105 - 1117 pp.

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.

blow-up , Logarithmic Sobolev-Folland-Stein inequality , non-blow-up , stratified groups

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Department of Mathematics, Nazarbayev University, 53 Kabanbay Batyr Avenue, Nur-Sultan, 010000, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium
Al-Farabi Kazakh National University, 71 Al-Farabi Avenue, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, 125 Pushkin Street, Almaty, 050010, Kazakhstan

Department of Mathematics
Department of Mathematics: Analysis
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling

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