Geodesic
Finding the moment functions of a~solution of the two-dimensional diffusion equation with random coefficients
Izvestiya. Mathematics , Tome 74 (2010) no. 6, pp. 1127-1154

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The problem of finding the moment functions of a solution of an initial-value problem with random coefficients for the two-dimensional diffusion equation reduces to a deterministic initial-value problem involving ordinary and variational derivatives. Formulae for the moment functions of a solution are obtained for uniformly distributed and for Gaussian random coefficients.
Keywords: moment functions, variational derivative, equations with random coefficients.
Mots-clés : diffusion equation 
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M. M. Borovikova; V. G. Zadorozhniy. Finding the moment functions of a~solution of the two-dimensional diffusion equation with random coefficients. Izvestiya. Mathematics , Tome 74 (2010) no. 6, pp. 1127-1154. http://geodesic.mathdoc.fr/item/IM2_2010_74_6_a1/