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].

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2018.03.002
Mots-clés : 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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  • J. Vanterler da C. Sousa; D. S. Oliveira Blow-up of solutions to fractional quasilinear hyperbolic problem, Analysis and Mathematical Physics, Volume 15 (2025) no. 2 | DOI:10.1007/s13324-025-01033-1
  • Menglan Liao; Zhong Tan Blow‐up and energy decay for a class of wave equations with nonlocal Kirchhoff‐type diffusion and weak damping, Mathematical Methods in the Applied Sciences, Volume 47 (2024) no. 1, p. 516 | DOI:10.1002/mma.9668
  • Yuzhu Han; Qi Li Lifespan of solutions to a damped plate equation with logarithmic nonlinearity, Evolution Equations Control Theory, Volume 11 (2022) no. 1, p. 25 | DOI:10.3934/eect.2020101

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