On the solutions of stochastic initial-value problems in continuum mechanics
type: Item
instance of: scholarly article
title: On the solutions of stochastic initial-value problems in continuum mechanics
zbMATH Open document ID: 0582.60066
DOI: 10.1016/0022-247X(85)90307-5
author: G. Adomian
author: Dante Bigi
author: R. Riganti
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 3932137
zbMATH Keywords: nonlinear hyperbolic equation
zbMATH Keywords: decomposition method
zbMATH Keywords: perturbation procedure
zbMATH Keywords: sequence of stochastic linear problems
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3932137