Comptes Rendus
no. 5
Blow-up of solutions to a quasilinear wave equation for high initial energy
Fang Li1; Fang Liu2 
1 School of Mathematics, Jilin University, Changchun 130012, PR China
2 School of Basic Sciences, Changchun University of Technology, Changchun 130012, PR China
Comptes Rendus. Mécanique, Volume 346 (2018) no. 5, pp. 402-407.

This paper deals with blow-up solutions to a nonlinear hyperbolic equation with variable exponent of nonlinearities. By constructing a new control function and using energy inequalities, the authors obtain the lower bound estimate of the L2 norm of the solution. Furthermore, the concavity arguments are used to prove the nonexistence of solutions; at the same time, an estimate of the upper bound of blow-up time is also obtained. This result extends and improves those of [1,2].

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2018.03.002
Keywords: Viscoelastic hyperbolic equation, Energy estimate method, High initial energy

Fang Li 1; Fang Liu 2

1 School of Mathematics, Jilin University, Changchun 130012, PR China
2 School of Basic Sciences, Changchun University of Technology, Changchun 130012, PR China 
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Fang Li; Fang Liu. Blow-up of solutions to a quasilinear wave equation for high initial energy. Comptes Rendus. Mécanique, Volume 346 (2018) no. 5, pp. 402-407. doi : 10.1016/j.crme.2018.03.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.03.002/

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