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- W2563648412 abstract "Consider wave equations of the form begin{document}$begin{align*}u''(t)+ A^2u(t)=0end{align*}$ end{document} with $A$ an injective selfadjoint operator on a complex Hilbert space $mathcal{H}$. The kinetic, potential, and total energies of a solution $u$ are begin{document}$begin{align*}K(t)= | u'(t)|^2, P(t)= |Au(t)|^2, E(t) = K(t)+P(t).end{align*}$ end{document} Finite energy solutions are those mild solutions for which $E(t)$ is finite. For such solutions $E(t)= E(0)$, that is, energy is conserved, and asymptotic equipartition of energy begin{document}$begin{align*}lim_{t longrightarrow ± ∞}K(t) = lim_{t longrightarrow ± ∞}P(t) = frac{E(0)}{2}end{align*}$ end{document} holds for all finite energy mild solutions iff $e^{itA}longrightarrow 0$ in the weak operator topology. In this paper we present the first extension of this result to the case where $A$ is time dependent." @default.
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- W2563648412 date "2017-01-01" @default.
- W2563648412 modified "2023-10-18" @default.
- W2563648412 title "Equipartition of energy for nonautonomous wave equations" @default.
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- W2563648412 doi "https://doi.org/10.3934/dcdss.2017004" @default.
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