On the solutions of stochastic initial-value problems in continuum mechanics. (English) Zbl 0582.60066

The authors study the stochastic operator equation \[ (1)\quad L^{(2)}_{t,x}u+R^{(2)}_{t,x}u=f(t,\underline x,u,L^{(1)}_{t,x}u,r(\underline x,t;\omega),\eta) \]
\[ u(\underline x,t=0)=\psi_ 1(\underline x);\quad u_ t(\underline x;t=0)=\psi_ 2(\underline x), \] which is a mathematical model for a number of physical systems. Under some assumptions, too complex to be presented here, the equation (1) is investigated using a perturbation procedure leading to a sequence of stochastic linear problems solved by application of the known Adomian method in both cases where \(\eta\) is a small parameter and \(\eta\) is not small. The calculation of moments of the solutions is included.
Reviewer: D.Bobrowski


60H25 Random operators and equations (aspects of stochastic analysis)
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