Nonexistence of Global Solutions to a Class of Weakly Coupled Semilinear Double-Wave System with Nonlinear Terms

Blow-up of solutions to a class of weakly coupled semilinear double-wave system with nonlinear terms in the subcritical case is considered. By introducing some time-dependent functional associated with differential inequality methods, an iteration frame and the first lower bound of solutions are obtained. Then, blow-up of solutions to the Cauchy problem is proved via the iteration technique and slicing methods. Meanwhile, the upper bound of the lifespan for solutions is derived.