About second mixed moment functions for solution of diffusion equation with random coefficients

10.12737/5120 ◽  
2014 ◽  
Vol 2 (4) ◽  
pp. 83-86
Author(s):  
I. Dubrovskiy
Keyword(s):  
Diffusion Equation ◽  
Random Coefficients ◽  
Mixed Moment ◽  
Moment Functions

scholarly journals Differential Equation in a Banach Space Multiplicatively Perturbed by Random Noise

2017 ◽  
Vol 63 (4) ◽  
pp. 599-614
Author(s):  
V G Zadorozhniy ◽  
M A Konovalova
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Random Noise ◽  
Random Coefficients ◽  
First Order ◽  
The Cauchy Problem ◽  
Moment Functions ◽  
Nonhomogeneous Differential Equation ◽  
Variational Derivatives ◽  
The Moment

We consider the problem of finding the moment functions of the solution of the Cauchy problem for a first-order linear nonhomogeneous differential equation with random coefficients in a Banach space. The problem is reduced to the initial problem for a nonrandom differential equation with ordinary and variational derivatives. We obtain explicit formula for the mathematical expectation and the second-order mixed moment functions for the solution of the equation.

scholarly journals N-ORDER MOMENT FUNCTION FOR THE SOLUTION OF THE CAUCHY PROBLEM FOR DIFFUSION EQUATION WITH RANDOM COEFFICIENTS

2017 ◽  
Vol 17 (8) ◽  
pp. 5-20
Author(s):  
T.V. Besedina
Keyword(s):  
Cauchy Problem ◽  
Diffusion Equation ◽  
Three Dimensional ◽  
Random Coefficients ◽  
Moment Function ◽  
Order Moment ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Dimensional Diffusion ◽  
The Cauchy Problem

Formula for n-order moment function for the solution of the Cauchy problem for three-dimensional diffusion equation with random coefficients and random initial condition is derived.

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