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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.
In this work, we investigate the influence of general damping and potential terms on the blow-up and lifespan estimates for energy solutions to power-type semilinear wave equations. The space-dependent damping and potential functions are assumed to b
In this paper we study the initial boundary value problem for two-dimensional semilinear wave equations with small data, in asymptotically Euclidean exterior domains. We prove that if $1<ple p_c(2)$, the problem admits almost the same upper bound of
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 mixed nonlinearities $a |u_t|^p+b |u|^q$, posed on asymptotically Euclide
In this paper, we investigate the problem of blow up and sharp upper bound estimates of the lifespan for the solutions to the semilinear wave equations, posed on asymptotically Euclidean manifolds. Here the metric is assumed to be exponential perturb
We provide reversed Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds using cluster estimates for spectral projectors proved previously in such generality. As a consequence, we solve a problem lef