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We study the Cauchy problem associated with the equations governing a fluidloaded plate formulated on either the line or the half-line. We show that inboth cases the problem can be solved by employing the unified approach toboundary value problems introduced by on of the authors in the late 1990s. Theproblem on the full line was analysed by Crighton et. al. using a combinationof Laplace and Fourier transforms. The new approach avoids the technicaldifficulty of the a priori assumption that the amplitude of the plate is in$L^1_{dt}(R^+)$ and furthermore yields a simpler solution representation whichimmediately implies the problem is well-posed. For the problem on thehalf-line, a similar analysis yields a solution representation, but thisformula involves two unknown functions. The main difficulty with the half-lineproblem is the characterisation of these two functions. By employing theso-called global relation, we show that the two functions can be obtained viathe solution of a complex valued integral equation of the convolution type.This equation can be solved in closed form using the Laplace transform. Byprescribing the initial data $\eta_0$ to be in $H^3(R^+)$, we show that thesolution depends continuously on the initial data, and hence, the problem iswell-posed.

A Novel Method of Solution for the Fluid Loaded Plate