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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 be critical or short range, spherically symmetric perturbation. The blow up results and the upper bound of lifespan estimates are obtained by the so-called test function method. The key ingredient is to construct special positive solutions to the linear dual problem with the desired asymptotic behavior, which is reduced, in turn, to constructing solutions to certain elliptic eigenvalue problems.
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|
It is believed or conjectured that the semilinear wave equations with scattering space dependent damping admit the Strauss critical exponent, see Ikehata-Todorova-Yordanov cite{ITY}(the bottom in page 2) and Nishihara-Sobajima-Wakasugi cite{N2}(conje
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
We study semilinear damped wave equations with power nonlinearity $|u|^p$ and initial data belonging to Sobolev spaces of negative order $dot{H}^{-gamma}$. In the present paper, we obtain a new critical exponent $p=p_{mathrm{crit}}(n,gamma):=1+frac{4
This paper is concerned with the initial value problem for semilinear wave equation with structural damping $u_{tt}+(-Delta)^{sigma}u_t -Delta u =f(u)$, where $sigma in (0,frac{1}{2})$ and $f(u) sim |u|^p$ or $u |u|^{p-1}$ with $p> 1 + {2}/(n - 2 sig