Well‐posedness for the massive nonlinear wave equation on asymptotically AdS spacetimes. (8th July 2020)

• Record Type: Journal Article
• Authors: Guo, Boling; Liu, Fengxia
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 15(2020)
• Page Start: 8930
• Page End: 8944
• Publication Date: 2020-07-08
• Subjects: asymptotically AdS spacetime -- Breitenlohner and Freedman bound -- nonlinear Klein‐Gordon equation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6587
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we prove some well‐posedness theorems for the nonlinear massive wave equation (with the mass satisfying the Breitenlohner‐Freedman bound) on asymptotically anti‐de Sitter spaces. The solution is constructed by contraction mapping method and also as a limit of solutions to an initial boundary value problem with boundary at a finite location in spacetime by finally pushing the boundary out to infinity. The solution obtained is unique within the energy class.