Comptes Rendus
no. 4
Lower bound estimates of blow-up time for a quasilinear hyperbolic equation with superlinear sources
Ge Zu1 ; Fang Li1  
1 School of Mathematics, Jilin University, Changchun 130012, PR China
Comptes Rendus. Mécanique, Volume 348 (2020) no. 4, pp. 307-313.

This paper deals with the lower bound for blow-up solutions to a quasilinear hyperbolic equation with strong damping. An inverse Hölder inequality with a correction constant is employed to overcome the difficulty caused by the failure of the embedding inequality. Moreover, a lower bound for blow-up time is obtained by constructing a new control functional with a small dissipative term and by applying an inverse Hölder inequality as well as energy inequalities. This result gives a positive answer to the open problem presented in [1].

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Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmeca.9
Mots clés : Inverse Hölder inequality, Energy estimate method, Energy inequality, Lower bound estimate, Quasilinear hyperbolic equation

Ge Zu 1 ; Fang Li 1

1 School of Mathematics, Jilin University, Changchun 130012, PR China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Ge Zu; Fang Li. Lower bound estimates of blow-up time for a quasilinear hyperbolic equation with superlinear sources. Comptes Rendus. Mécanique, Volume 348 (2020) no. 4, pp. 307-313. doi : 10.5802/crmeca.9. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.9/

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