Abstract
Given a complex Hilbert space H, we establish a result on asymptotic energy equipartition for the abstract coupled system u t t + 2 F ( S ) v t + S 2 u = 0 v t t + 2 F ( S ) u t + S 2 v = 0 for (u,v):[0,∞)→H⊕H with selfadjoint S:D(S)→H and operator-valued damping F≥0. Both the kinetic and the potential energies of solutions contain interaction terms in the general case and are conveniently weighted to account for the presence of damping. A remarkable feature of the above system is that it is wellposed if and only if F is bounded, a fact that we also prove.
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