Equipartition of energy for nonautonomous damped wave equations
The kinetic and potential energies for the damped wave equation u00 + 2Bu0 + A2u = 0 (DWE) are defined by K(t) = ku0(t)k2, P(t) = kAu(t)k2, where A, B are suitable commuting selfadjoint operators. Asymptotic equipartition of energy means tlim →∞KP((tt)) = 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).
Discrete and Continuous Dynamical Systems - Series S
D'Abbicco, M., Girardi, G., Goldstein, G., Goldstein, J., & Romanelli, S. (2021). Equipartition of energy for nonautonomous damped wave equations. Discrete and Continuous Dynamical Systems - Series S, 14 (2), 597-613. https://doi.org/10.3934/dcdss.2020364