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

Ardak Kashkynbayev, Aidyn Kassymov (UGent) and Durvudkhan Suragan
(2023) QUAESTIONES MATHEMATICAE. 46(6). p.1105-1117
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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.
Keywords
Logarithmic Sobolev-Folland-Stein inequality, non-blow-up, blow-up, stratified groups, SOBOLEV INEQUALITIES

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MLA
Kashkynbayev, Ardak, et al. “Non-Blow-up and Blow-up Results to Heat Equations with Logarithmic Nonlinearity on Stratified Groups.” QUAESTIONES MATHEMATICAE, vol. 46, no. 6, 2023, pp. 1105–17, doi:10.2989/16073606.2022.2057368.
APA
Kashkynbayev, A., Kassymov, A., & Suragan, D. (2023). Non-blow-up and blow-up results to heat equations with logarithmic nonlinearity on stratified groups. QUAESTIONES MATHEMATICAE, 46(6), 1105–1117. https://doi.org/10.2989/16073606.2022.2057368
Chicago author-date
Kashkynbayev, Ardak, Aidyn Kassymov, and Durvudkhan Suragan. 2023. “Non-Blow-up and Blow-up Results to Heat Equations with Logarithmic Nonlinearity on Stratified Groups.” QUAESTIONES MATHEMATICAE 46 (6): 1105–17. https://doi.org/10.2989/16073606.2022.2057368.
Chicago author-date (all authors)
Kashkynbayev, Ardak, Aidyn Kassymov, and Durvudkhan Suragan. 2023. “Non-Blow-up and Blow-up Results to Heat Equations with Logarithmic Nonlinearity on Stratified Groups.” QUAESTIONES MATHEMATICAE 46 (6): 1105–1117. doi:10.2989/16073606.2022.2057368.
Vancouver
1.
Kashkynbayev A, Kassymov A, Suragan D. Non-blow-up and blow-up results to heat equations with logarithmic nonlinearity on stratified groups. QUAESTIONES MATHEMATICAE. 2023;46(6):1105–17.
IEEE
[1]
A. Kashkynbayev, A. Kassymov, and D. Suragan, “Non-blow-up and blow-up results to heat equations with logarithmic nonlinearity on stratified groups,” QUAESTIONES MATHEMATICAE, vol. 46, no. 6, pp. 1105–1117, 2023.
@article{8752857,
  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.}},
  author       = {{Kashkynbayev, Ardak and Kassymov, Aidyn and Suragan, Durvudkhan}},
  issn         = {{1607-3606}},
  journal      = {{QUAESTIONES MATHEMATICAE}},
  keywords     = {{Logarithmic Sobolev-Folland-Stein inequality,non-blow-up,blow-up,stratified groups,SOBOLEV INEQUALITIES}},
  language     = {{eng}},
  number       = {{6}},
  pages        = {{1105--1117}},
  title        = {{Non-blow-up and blow-up results to heat equations with logarithmic nonlinearity on stratified groups}},
  url          = {{http://doi.org/10.2989/16073606.2022.2057368}},
  volume       = {{46}},
  year         = {{2023}},
}
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