2.29.5. Three parts of resulting solution

The solution G(y,z), described by Eq. 2.29.5, has been obtained by Fedorov and Stehlik (1997) using the method of the direct and inverse Fourier-Laplace transform and it consists of three terms:

The first component describes a contribution of the unscattered particles which exponentially decreases with time t:

A contribution of the scattered particles can be divided into two parts. One, the non-diffusive term Gso (y,T), also exponentially decreases with time, and another term, G'd (y,T), has a leading meaning in the diffusive limit of t >> 1. Namely, the non-diffusive term reads

xJ Jdrf¥(y,z,rilS{T)-S(y)]+ Jdnx¥(y,T,n)[(y/n)-S(y)] J, (2.29.8)

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