Lifespan estimates of solutions to semilinear wave equations with damping term on the exterior domain

ABSTRACT

Initial-boundary value problems for semilinear wave equations with damping term and Neumann boundary conditions on the exterior domain are investigated. In sub-critical and critical cases, blow-up and upper bound lifespan estimates of solutions to the problems which contain power nonlinearity $|u{|}^q$, derivative nonlinearity $|u_t{|}^p$, combined nonlinearity $|u_t{|}^p+|u{|}^q$, respectively, are derived by applying test function technique and iterative method. The novelty is that lifespan estimates of solutions are associated with the well-known Strauss conjecture and Glassey conjecture.

KEYWORDS:

• Semilinear wave equations
• Neumann boundary conditions
• lifespan estimates
• test function technique
• iterative method

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35L70
• 58J45

Acknowledgements

The author, Sen Ming, would like to express his sincere thanks to Professor Yi Zhou for his guidance and encouragement during his postdoctoral study at Fudan University. The author Sen Ming also would like to express his sincere thanks to Professor Ning-An Lai for his helpful suggestions and discussions.

Disclosure statement

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

Additional information

Funding

The project is supported by the Natural Science Foundation of Shanxi Province of China [grant number 201901D211276], the Fundamental Research Program of Shanxi Province [grant number 20210302123045] and the National Natural Science Foundation of P. R. China [grant number 11471263].