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Summary:
The transport equation for the neutron density in an infinite absorbing and non-multiplying medium is discussed provided the initial distribution is known. The macroscopic effective cross-sections and sources are considered to be functions of spatial, angular, energetic and time coordinates. Two theorems asserting the existence and uniqueness of the solution of the problem are presented.
References:
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[3] I. Vidav: Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator. Journ. of Math. Ann. and Appl. 22 (1968), 144-155. DOI 10.1016/0022-247X(68)90166-2 | MR 0230531 | Zbl 0155.19203
[4] J. Potoček: Iterative methods. (reports lectured at Mathematical Institute of Charles's University) Prague 1958-1959.
[5] Э. Камке: Справочник по дифференциальным уравнениям в частных производных первого порядка. Москва 1966. Zbl 1155.78304
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