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Advances in Differential Equations and Control Processes

is solved, in two and three dimensions. It is pointed out that the behavior of the solution is controlled by the definite integral of

for time, assuming that the diffusion process is taking place at the time interval

The physical meaning of the solution is that at time t, the value of the quantity which is involved in the diffusion process depends on the mean value of

and not on its specific variation with time. The conclusions of this paper may be useful in modeling diffusion processes in various fields of geosciences such as hydrology, geomorphology and soil or atmospheric pollution.

Advances in Differential Equations and Control Processes
Volume 5, Issue 1, Pages 37 - 47 (February 2010)

SOLUTION OF THE LINEAR DIFFUSION EQUATION WITH A TIME DEPENDENT DIFFUSION COEFFICIENT, IN TWO AND THREE DIMENSIONS
Georgios Aim. Skianis and Efthimia Verikiou

Abstract:
In the present paper, the diffusion equation for a time dependent diffusion coefficient

is solved, in two and three dimensions. It is pointed out that the behavior of the solution is controlled by the definite integral of

for time, assuming that the diffusion process is taking place at the time interval

The physical meaning of the solution is that at time t, the value of the quantity which is involved in the diffusion process depends on the mean value of

Keywords and phrases: diffusion equation, diffusion coefficient, Fourier transform, radial Fourier transform.

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