Abstract:In this work, we investigate the problem of finite time blow up as well as the upper bound estimates of lifespan for solutions to small-amplitude semilinear wave equations with time dependent damping and potential, and mixed nonlinearities c 1 |ut| p + c 2 |u| q , posed on asymptotically Euclidean manifolds, which is related to both the Strauss conjecture and the Glassey conjecture.
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