Abstract
Damped wave equations with random excitation describing the vibrations of a string with a dissipative force are discussed. The sources of such random disturbances are either an initial white noise or a Gaussian random forcing. Let ue(t,x) be the displacement at time t of a point x on a string, where the time variable t≥0, and the space variable x∈R. The random fields ue(t,x) are analyzed in the limit as the intensity of the noise e tends to zero, and law of large numbers type results are given for the deviations.
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