2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140460In this article we construct the fundamental solutions for the wave equation arising in the de Sitter model of the universe. We use the fundamental solutions to represent solutions of the Cauchy problem and to prove the $L^p-L^q$-decay estimates for the solutions of the equation with and without a source term.36 pages; http://www.math.uni-potsdam.de/prof/a_partdiff/prepr/2007_06.pdfAnalysis of PDEsMathematical Physics35C15; 35L05; 35Q75; 35L15text