Local energy decay of solutions to the wave equation for nontrapping metrics
type: Item
instance of: scholarly article
title: Local energy decay of solutions to the wave equation for nontrapping metrics
zbMATH Open document ID: 1061.58024
DOI: 10.1007/BF02385487
published in: Arkiv för Matematik
publication date: 2004-09-28T00:00:00Z
review text: The paper analyzes asymptotic decay of local energy of a solution to a generalized linear wave equation on a Riemannian manifold of an arbitrary dimension, i.e., energy calculated in a bounded part of the manifold, in the case when the metric on the manifold is nontrapping, i.e., the energy initially confined to a bounded area decays because of emission of radiation. As a result, an estimate is obtained for the decay law of the local energy as a negative power of time. The proofs are based on resolvent estimates for high-frequency components of the wave field. The general results are applied to asymptotically Euclidean spaces, and some other cases of particular interest (the model with long-range nonnegative potentials).
reviewed by: B. A. Malomed
Mathematics Subject Classification ID: 58J45
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35L90
zbMATH DE Number: 2103856
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: emission of radiation
zbMATH Keywords: resolvent estimates
author: Georgi Vodev
MaRDI profile type: Publication
cites work: Uniform estimates of the resolvent of the Laplace-Beltrami operator on infinite volume Riemannian manifolds. II
cites work: Singularities of boundary value problems. II
cites work: Semiclassical estimates in asymptotically Euclidean scattering
cites work: UNIFORM ESTIMATES OF THE RESOLVENT OF THE LAPLACE –BELTRAMI OPERATOR ON INFINITE VOLUME RIEMANNIAN MANIFOLDS WITH CUSPS
description: scientific article; zbMATH DE number 2103856