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The problem of flattening the reactor specific output for the case of homogenized thermal critical reactor fueled with natural uranium is mathematically formulated (in the two-groups diffusion approximation and for onedimensional geometries) in the article. It is shown that this problem leads to a quasilinear biharmonic Cauchy's problem having a twoparametrical family of solutions $N(x;N_0,N"_0)$. The existence and stability of these solutions and the possibility of the optimization of the total reactor output by a proper choice of the parameters $N_0,N"_0$ is investigated.
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[5] S. Lefschetz: Differential Equations: Geometric Theory. Interscience Publ., New York, London 1957. MR 0094488 | Zbl 0080.06401
[6] K. Meyer: Private communication (at the occasion of the Second German-Czechoslovak Colloquium on Reactor Physics, held at Baabe, Rügen, GDR, October 66). Zbl 1170.01377
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