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 / D'Abbicco, M; Girardi, G; Goldstein, Gr; Goldstein, Ja; Romanelli, S. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 14:2(2021), pp. 597-613. [10.3934/dcdss.2020364]
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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
