Lifespan of solutions to semilinear damping wave equations in de Sitter spacetime

This paper studies blowup phenomena for two kind of initial value problem of semilinear damping wave equations in de Sitter spacetime. The first problem comes from the latter problem of conjecture of Strauss in de Sitter Spacetime, and the second problem arises from the latter problem of conjecture of Glassey in de Sitter Spacetime. We give blowup and lifespan of solutions on those two problems. Comparing with non-damping case established in Yan (2018), one can see that the damping term with a positive bounded time-dependent coefficient does not effect blowup of solutions. Meanwhile, we establish a new ODE blowup result concerning damping term. (C) 2019 Elsevier Ltd. All rights reserved.