Blow-up of weak solutions for a higher-order heat equation with logarithmic nonlinearity

Blow-up of weak solutions for a higher-order heat equation with logarithmic nonlinearity

This paper deal with the initial boundary value problem for a higher-order heat equation with logarithmic source term ut + (-Δ)m u - Δut = uk-2 uln |u|. We obtain blow-up of weak solutions in the finite time, by employing potential well technique and concave technique. In addition, the upper bound o...

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Veröffentlicht in:Mathematical notes (Miskolci Egyetem (Hungary)) 2023, Vol.24 (2), p.749-762
Hauptverfasser: Cömert, Tuğrul, Pişkin, Erhan
Format: Artikel
Sprache:eng
Schlagworte:
Boundary value problems
Cauchy problems
Logarithms
Thermodynamics
Upper bounds
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Zusammenfassung:This paper deal with the initial boundary value problem for a higher-order heat equation with logarithmic source term ut + (-Δ)m u - Δut = uk-2 uln |u|. We obtain blow-up of weak solutions in the finite time, by employing potential well technique and concave technique. In addition, the upper bound of blow-up time is considered. This improves and extends some previous studies.
ISSN:1787-2405
1787-2413
DOI:10.18514/MMN.2023.4014