Abstract
We present a Hilbert space analytical rigorous method to solve globally a class of important abstract wave equations in mathematical physics of continuum mechanics. We show its usefulness by proposing some sort of Trotter–Kato–Feynman method to analyze the usual wave motion in . We besides produce a proof for the exponential decay of the total energy associated to a planar magnetoelastic wave motion in an electric dispersive medium. As a last result of our work, we present the existence and uniqueness of an abstract Klein–Gordon functional wave equation by means of Hilbert space techniques.
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