On finding moment functions for the solution of the Cauchy problem for the diffusion equation with random coefficients

2002 ◽  
Vol 66 (4) ◽  
pp. 771-788 ◽  
Author(s):  
V G Zadorozhnii
Keyword(s):  
Cauchy Problem ◽  
Diffusion Equation ◽  
Random Coefficients ◽  
The Cauchy Problem ◽  
Moment Functions

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.

scholarly journals Existence of Positive Solution to the Cauchy Problem for a Fractional Diffusion Equation with a Singular Nonlinearity

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Ailing Shi ◽  
Shuqin Zhang
Keyword(s):  
Cauchy Problem ◽  
Diffusion Equation ◽  
Positive Solution ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Successive Approximation Method ◽  
Fractional Diffusion Equations ◽  
Singular Nonlinearity ◽  
Analysis Technique ◽  
The Cauchy Problem

Fractional diffusion equations describe an anomalous diffusion on fractals. In this paper, by means of the successive approximation method and other analysis technique, we present a local positive solution to Cauchy problem for a fractional diffusion equation with singular nonlinearity. The fractional derivative is described in the Caputo sense.

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