Research Article

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

Published in: Quaestiones Mathematicae
Volume 46 , issue 6 , 2023 , pages: 1105–1117

DOI: 10.2989/16073606.2022.2057368

Author(s): Ardak Kashkynbayev Nazarbayev University, Kazakhstan , Aidyn Kassymov Ghent University, Belgium , Durvudkhan Suragan Nazarbayev University, Kazakhstan

Keywords: 35B44 , 22E30 , 35H20 , Logarithmic Sobolev-Folland-Stein inequality , non-blow-up , blow-up , stratified groups

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Abstract

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.

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