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Summary:
In the paper the following problem of the nuclear reactor theory is mathematically formulated (in the two-group diffusion approximation and for multidimensional geometries): For a prescribed flux $\Phi$ of thermal neutrons in the core $\Omega$ of the finite homogenized reactor the distribution $M(x)$ of the fuel concentration in $\Omega$ which induces this given flux $\Phi$ in the reactor core $\Omega$ is to be determined. The conditions (in particular on the form of the boundary $\Omega$ of the core $\Omega$ as well as of the boundary $\Lambda$ of its reflector $\Lambda$) are given which are sufficient for the existence of a unique solution of this problem and, especially, also for the existence of a unique solution in the special case of flattened thermal neutron flux $\Phi = \Phi_0 = const$ in the reactor core $\Omega$ which is of practical significance for it yields the minimum of the critical mass.
References:
[1] V. Bartošek R. Zezula: Flat Flux in a Slab reactor with Natural Uranium. Report ÚJV ČSAV 1310 (1965).
[2] R. Zezula: A sufficient condition for the flattening of thermal neutron flux and some related problems. (in onedimensional geometries). Apl. Mat. 14 (1969), 134-145.
[3] A. Miasnikov R. Zezula: Radial flux flattening in a cylindrical reactor with natural uranium. (In Czech - Internal Report OTRF, ÚJV ČSAV).
[4] V. Bartošek R. Zezula: Flat flux in a slab reactor with natural uranium. Journal of Nuclear Energy Parts A/B, 1966, vol. 20, pp. 129-139. DOI 10.1016/0368-3230(66)90023-1
[5] M. Hron V. Lelek: Flux flattening by means of a nonuniform fuel distribution in a slab reactor with finite reflector. Report ÚJV ČSAV 1660 (1966).
[6] V. Bartošek R. Zezula: Stability of flat thermal flux in a slab reactor. Apl. Mat. 13 (1968), 367-375. MR 0243795
[7] Ladyzhenskaya O. A., Uraľceva N. N.: Linear and quasilinear equations of elliptic type. Nauka, Moscow 1964 (in russian). MR 0509265
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