Blow-up for a coupled system of semilinear wave equations with scattering dampings and combined nonlinearities

Abstract

The blow-up of solutions to a coupled system of semilinear wave equations in the sub-critical and critical cases is investigated. The system contains scattering dampings and combined nonlinearities. The upper bound lifespan estimates of solutions which are related to the indexes of nonlinear terms are established by applying the functional method and iteration technique.

Keywords:

• Coupled system
• scattering dampings
• combined nonlinearities
• blow-up
• lifespan estimates

2010 Mathematics Subject Classification:

• 35G25·35L15

Acknowledgments

The author Sen Ming would like to express his sincere thank to Professor Yi Zhou for his guidance and encouragements during the postdoctoral study in Fudan University. The author Sen Ming also would like to express his sincere thank to Professor Ning-An Lai for his helpful suggestions and discussions. The project is supported by Natural Science Foundation of Shanxi Province of China (No. 201901D211276), Science Foundation of North University of China (No. 2017030, No. 13011920) and National Natural Science Foundation of P. R. China (No. 11471263).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The project is supported by Natural Science Foundation of Shanxi Province of China (Grant Number 201901D211276), Science Foundation of North University of China (Grant Numbers 2017030 and 13011920) and National Natural Science Foundation of P. R. China (Grant Number 11471263).