Comptes Rendus
no. 6
An inverse Hölder inequality and its application in lower bound estimates for blow-up time
Bin Guo1
1 School of Mathematics, Jilin University, Changchun 130012, PR China
Comptes Rendus. Mécanique, Volume 345 (2017) no. 6, pp. 370-377.

This paper deals with the lower bound for blow-up solutions to a nonlinear viscoelastic hyperbolic equation. An inverse Hölder inequality with the correction constant is employed to overcome the difficulty caused by the failure of the embedding inequality W01,r(Ω)↪L2α−2(Ω)(r⁎+22<α<r⁎=NrN−r) and the lack of a version of the Gagliardo–Nirenberg inequality. Moreover, a lower bound for blow-up time is obtained by establishing a first-order differential inequality. This result is a continuation of an earlier work [1].

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2017.04.002
Mots clés : Viscoelastic hyperbolic equation, Energy estimate method, Lower bound estimate
Bin Guo 1

1 School of Mathematics, Jilin University, Changchun 130012, PR China 
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Bin Guo. An inverse Hölder inequality and its application in lower bound estimates for blow-up time. Comptes Rendus. Mécanique, Volume 345 (2017) no. 6, pp. 370-377. doi : 10.1016/j.crme.2017.04.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.04.002/

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