Fu, Song-RenNing, Zhen-Hu2023-04-252023-04-252022-08-05Fu, S. R., & Ning, Z. H. (2022). Stabilization of the critical nonlinear Klein-Gordon equation with variable coefficients on R3. <i>Electronic Journal of Differential Equations, 2022</i>(59), pp. 1-18.1072-6691https://hdl.handle.net/10877/16649We prove the exponential stability of the defocusing critical semilinear wave equation with variable coefficients and locally distributed damping on R3. The construction of the variable coefficients is almost equivalent to the geometric control condition. We develop the traditional Morawetz estimates and the compactness-uniqueness arguments for the semilinear wave equation to prove the unique continuation result. The observability inequality and the exponential stability are obtained subsequently.Text18 pages1 file (.pdf)enAttribution 4.0 InternationalCritical semilinear wave equationVariable coefficientsStabilityMorawetz estimatesRiemannian geometryUnique continuationArticle