Blow-Up Results for a Weakly Coupled System of Semilinear Wave Equations in de Sitter Spacetime

The main goal of this paper is to study blow-up of solutions of a weakly coupled system for semilinear wave equations with damping terms and mass terms in the de Sitter spacetime. The exponential, polynomial, and logarithmic growth of time-dependent factors in nonlinear terms are investigated by using iterative methods, respectively. Upper bound lifespan estimates of solutions to the problem are established. To the best of our knowledge, the results in Theorems 1.1-1.3 are new. In particular, the critical curve for exponents (p, q) in nonlinear terms in this problem is same as the critical curve for a weakly coupled system of semilinear wave equations with power nonlinearities. In addition, wave trends are expressed by numerical simulation.