A Parametrix for the Fundamental Solution of the Klein-gordon Equation on Asymptotically De Sitter Spaces

A Strichartz estimate for de Sitter space

We demonstrate a family of Strichartz estimates for the conformally invariant KleinGordon equation on a class of asymptotically de Sitter spaces with C2 metrics by using well-known local Strichartz estimates and a rescaling argument. This class of metrics includes de Sitter space. We also give an application of the estimates to a semilinear Klein-Gordon equation on these spaces.

B-SPLINE COLLOCATION APPROACH FOR SOLUTION OF KLEIN-GORDON EQUATION

We develope a numerical method based on B-spline collocation method to solve linear Klein-Gordon equation. The proposed scheme is unconditionally stable. The results of numerical experiments have been compared with the exact solution to show the efficiency of the method computationally. Easy and economical implementation is the strength of this approach.  

Numerical solution of Klein-Gordon equation by using the Adomian's decomposition and variational iterative methods

The Wave Equation on Asymptotically Anti-de Sitter Spaces

In this paper we describe the behavior of solutions of the KleinGordon equation, ( g + λ)u = f , on Lorentzian manifolds (X, g) which are anti-de Sitter-like (AdS-like) at infinity. Such manifolds are Lorentzian analogues of the so-called Riemannian conformally compact (or asymptotically hyperbolic) spaces, in the sense that the metric is conformal to a smooth Lorentzian metric ĝ on X, where X ...

Global Analysis of Quasilinear Wave Equations on Asymptotically De Sitter Spaces

We establish the small data solvability of suitable quasilinear wave and Klein-Gordon equations in high regularity spaces on a geometric class of spacetimes including asymptotically de Sitter spaces. We obtain our results by proving the global invertibility of linear operators with coefficients in high regularity L2-based function spaces and using iterative arguments for the nonlinear problems....