The kinetic and potential energies for the damped wave equationu '' + 2Bu' + A(2)u = 0 (DWE)are defined byK(t) = parallel to u'(t)parallel to(2), P(t) = parallel to Au(t)parallel to(2),where A, B are suitable commuting selfadjoint operators. Asymptotic equipar tition of energy meanslim(t ->infinity) 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
Girardi, G;
2021-01-01
Abstract
The kinetic and potential energies for the damped wave equationu '' + 2Bu' + A(2)u = 0 (DWE)are defined byK(t) = parallel to u'(t)parallel to(2), P(t) = parallel to Au(t)parallel to(2),where A, B are suitable commuting selfadjoint operators. Asymptotic equipar tition of energy meanslim(t ->infinity) 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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