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

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.