Abstract:
Moments of solutions of boundary value problems for evolution equations with random parameters (that is, coefficients, right-hand sides, and/or initial conditions) satisfy infinite systems of partial differential equations. Suppose that the following two conditions hold: 1) The operator in the boundary value problem is analytic, and the part of it linear in the unknown function is nondegenerate. 2) The random fluctuations in the parameters of the problem are sufficiently small. Then the solutions of the finite closed systems obtained from the infinite system of moment equations by equating all the moments of order greater than some $N$ to zero are approximate solutions of the original infinite system that converge to the exact solution as $N\to\infty$. Boundary value problems for quasilinear parabolic equations, nonlinear wave equations, Navier–Stokes systems, and so on are considered as examples.
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