The kinetic and potential energies for the damped wave equation u'' + 2Bu' + A^2u = 0 (DWE) are defined by K(t) = ||u'(t)||^2, P(t) = ||Au(t)||^2, where A,B are suitable commuting selfadjoint operators. Asymptotic equipartition of energy means lim_{t\to\infty} K(t)/P(t) = 1 (AEE) for all (finite energy) non-zero solutions of (DWE). The main result of this paper is the proof of a result analogous to (AEE) for a nonautonomous version of (DWE).
Equipartition of energy for nonautonomous damped wave equations
Marcello D'Abbicco;Silvia Romanelli
2021-01-01
Abstract
The kinetic and potential energies for the damped wave equation u'' + 2Bu' + A^2u = 0 (DWE) are defined by K(t) = ||u'(t)||^2, P(t) = ||Au(t)||^2, where A,B are suitable commuting selfadjoint operators. Asymptotic equipartition of energy means lim_{t\to\infty} K(t)/P(t) = 1 (AEE) for all (finite energy) non-zero solutions of (DWE). The main result of this paper is the proof of a result analogous to (AEE) for a nonautonomous version of (DWE).File in questo prodotto:
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