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We study the global existence of solutions to semilinear damped wave equations in the scattering case with derivative power-type nonlinearity on (1+3) dimensional nontrapping asymptotically Euclidean manifolds. The main idea is to exploit local energy estimate, together with local existence to convert the parameter $mu$ to small one.
We study the global existence of solutions to semilinear wave equations with power-type nonlinearity and general lower order terms on $n$ dimensional nontrapping asymptotically Euclidean manifolds, when $n=3, 4$. In addition, we prove almost global e
This paper is concerned with the nonlinear damped wave equation on a measure space with a self-adjoint operator, instead of the standard Laplace operator. Under a certain decay estimate on the corresponding heat semigroup, we establish the linear est
In this paper, we study the semilinear wave equations with the inverse-square potential. By transferring the original equation to a fractional dimensional wave equation and analyzing the properties of its fundamental solution, we establish a long-tim
In this paper, we prove the global existence for some 4-D quasilinear wave equations with small, radial data in $H^{3}times H^{2}$. The main idea is to exploit local energy estimates with variable coefficients, together with the trace estimates.
In this paper, we investigate the global behaviors of solutions to defocusing semilinear wave equations in $mathbb{R}^{1+d}$ with $dgeq 3$. We prove that in the energy space the solution verifies the integrated local energy decay estimates for the fu