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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.
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[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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