L^p′–L^p decay estimates of solutions to the wave equation with a short-range potential

Article type: Research Article

Authors: Cuevas, Claudio | Vodev, Georgi

Affiliations: Departamento de Matemática, Universidade Federal de Pernambuco, CEP. 50540-740 Recife-Pe, Brazil E-mail: cch@dmat.ufpe.br | Département de Mathématiques, Université de Nantes, UMR 6629 du CNRS, 2, rue de la Houssinière, BP 92208, 44332 Nantes Cedex 03, France E-mail: georgi.vodev@math.univ-nantes.fr

Abstract: We obtain large time decay of the Lp norms, 2<p<+∞, of solutions to the wave equation with a real-valued potential which decays slowly at infinity. This extends previous results by Beals and Strauss [Comm. Partial Differential Equations 18 (1993), 1365–1397] and Georgiev and Visciglia [Comm. Partial Differential Equations 28 (2003), 1325–1369].

Journal: Asymptotic Analysis, vol. 46, no. 1, pp. 29-42, 2006