INVERSE SOURCE PROBLEM FOR KLEIN-GORDON EQUATION IN DE SITTER SPACE-TIME (Analysis of inverse problems through partial differential equations and related topics)

Abstract

De Sitter space-time is a solution of the vacuum Einstein equation with a positive cosmological constant in Euclidean space. We prove a uniqueness theorem to determine a time-independent source term for the Klein-Gordon equation in de Sitter space-time up to a neighborhood of an open subset when the mass in the equation has a particular value. We establish a new method based on the Duhamel's principle and theory of distributions with compact supports to deal with inverse problems for such equations having time-dependent coefficients.