Semilinear wave equations on asymptotically de Sitter, Kerr-de Sitter and Minkowski spacetimes

摘要: In this paper we show the small data solvability of suitable semilinear wave and Klein-Gordon equations on geometric classes spaces, which include so-called asymptotically de Sitter Kerr-de as well Minkowski spaces. These spaces allow general infinities, called conformal infinity in setting; type setting is that non-trapping Lorentzian scattering metrics introduced by Baskin, Vasy Wunsch. Our results are obtained showing global Fredholm property, indeed invertibility, underlying linear operator L^2-based function also possess appropriate algebra or more complicated multiplicative properties. The framework based b-analysis, sense Melrose, context to describe asymptotic behavior solutions equations. An interesting feature analysis resonances, namely poles inverse Mellin transformed b-normal operator, `quantum' (not purely symbolic) objects, play an important role.