On the solutions of stochastic initial-value problems in continuum mechanics

This work deals with the analysis of a class of initial-value problems for nonlinear hyperbolic equations with stochastic process coefficients and four time-space independent variables. A perturbation procedure is developed, leading to a sequence of stochastic, partial differential equations which are solved by application of the Adomian decomposition method. A pertinent application in mechanics is also considered, and quantitative results are presented and discussed.