Asymptotic equipartition rate for wave motion in an even number of space dimensions
type: Item
instance of: scholarly article
title: Asymptotic equipartition rate for wave motion in an even number of space dimensions
zbMATH Open document ID: 0619.35067
DOI: 10.1016/0022-247X(86)90203-9
author: G. Dassios
author: Manoussos Grillakis
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: An energy conserving wave which is initially confined in a sphere of finite radius is propagating in a \(2\ell\)-dimensional space. It is proved that if the Cauchy data have \(\ell +2\) continuous derivatives then the difference between the potential and the kinetic energy has the asymptotic rate of decay \(t^{-2(\ell +\lambda)}\) as time \(t\to +\infty\), where \(\lambda\) depends on the order of the first nonvanishing moment of the Cauchy data. In other words, the rate at which asymptotic equipartition of energy is achieved depends not only on the number of space dimensions but also on how symmetrical the initial disturbance is distributed around the origin.
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 4004759
zbMATH Keywords: energy conserving wave
zbMATH Keywords: Cauchy data
zbMATH Keywords: potential
zbMATH Keywords: kinetic energy
zbMATH Keywords: rate of decay
zbMATH Keywords: asymptotic equipartition
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4004759