文章基本信息

标题：Equipartition of energy for higher-order hyperbolic equations
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作者：Jerome A. Goldstein ; James T. Sandefur
期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1981
卷号：78
期号：2
页码：698-698
DOI：10.1073/pnas.78.2.698
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Let A0, A1...,A2N-1 be commuting skew-adjoint operators on a Hilbert space [unk]. Then the equation {Pi}j=02N-1 (d/dt - Aj)v(t) = 0 (t real) admits equipartition of energy [in the sense that the jth partial energy Ej(t) of any solution at time t satisfies limt[->]{+/-}{infty}Ej(t) = 2-N{middle dot}(total energy) for each of the 2N values of j] if and only if the closure Bjk of Aj - Ak satisfies weak-operator-limit exp(tBjk) = 0 as t [->] {+/-}{infty} whenever j [!=] k.
关键词：hyperbolic partial differential equations ; asymptotic behavior ; equations in Hilbert space