Bai, Yige; Liu, Mengyun Global existence for semilinear damped wave equations in the scattering case. (English) Zbl 1424.35237 Differ. Integral Equ. 32, No. 3-4, 233-248 (2019). The authors study the Cauchy problem to the equation \(u_{tt}-\Delta_{g}u+\mu(1+t)^{-\beta}u_t=| u_t|^p,\) where \(\beta >1\) and \((\mathbb R^n,g)\) is a non-trapping asymptotically Euclidean manifold. Under some assumptions on \(\beta, p, \mu\) and the manifold \((\mathbb R^n,g)\) the global existence of the problem for small initial data is proved. The solution is obtained as a limit of the solutions to damped wave equations. Reviewer: Marie Kopáčková (Praha) Cited in 2 Documents MSC: 35L05 Wave equation 35L15 Initial value problems for second-order hyperbolic equations 35L71 Second-order semilinear hyperbolic equations Keywords:small initial data; Cauchy problem; non-trapping asymptotically Euclidean manifold; wave equation; energy estimate; boundedness × Cite Format Result Cite Review PDF Full Text: arXiv