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In this work, we investigate the problem of finite time blow up as well asthe upper bound estimates of lifespan for solutions to small-amplitudesemilinear wave equations with time dependent damping and potential, and mixednonlinearities $c_1 |u_t|^p+c_2 |u|^q$, posed on asymptotically Euclideanmanifolds, which is related to both the Strauss conjecture and the Glasseyconjecture.

Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds