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Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds (2104.08497v2)
Published 17 Apr 2021 in math.AP
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 $c_1 |u_t|p+c_2 |u|q$, posed on asymptotically Euclidean manifolds, which is related to both the Strauss conjecture and the Glassey conjecture.