Lower bound estimates of blow-up time for a quasilinear hyperbolic equation with superlinear sources
- Resource Type
- article
- Authors
- Zu, Ge; Li, Fang
- Source
- Comptes Rendus. Mécanique, Vol 348, Iss 4, Pp 307-313 (2020)
- Subject
- Inverse Hölder inequality
Energy estimate method
Energy inequality
Lower bound estimate
Quasilinear hyperbolic equation
Materials of engineering and construction. Mechanics of materials
TA401-492
- Language
- English
French
- ISSN
- 1873-7234
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].