Abstract
Let A0, A1,...,A2N-1 be commuting skew-adjoint operators on a Hilbert space [unk]. Then the equation Πj=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→±∞Ej(t) = 2-N·(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 → ±∞ whenever j ≠ k.
Keywords: hyperbolic partial differential equations, asymptotic behavior, equations in Hilbert space
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PDFPage 698
