Geodesic
Onedimensional homogenized reactor with natural uranium and with flattened specific output
Applications of Mathematics, Tome 14 (1969) no. 4, pp. 323-336

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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.
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. 
Zezula, Rostislav. Onedimensional homogenized reactor with natural uranium and with flattened specific output. Applications of Mathematics, Tome 14 (1969) no. 4, pp. 323-336. doi: 10.21136/AM.1969.103239
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[1] V. Bartošek R. Zezula: Flat Flux in a Slab Reactor with Natural Uranium. Journal of Nuclear Energy Parts A/B, 1966, Vol. 20, pp. 129-134. | DOI

[2] V. Bartošek R. Zezula: Stability of flat thermal Flux in a slab reactor. Apl. Mat. 13 (1968), 367-375. | MR

[3] 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.

[4] R. Bellman: Stability Theory of Differential Equations. Russian translation, Izd. Inostr. Lit., Moskva 1954. | MR

[5] S. Lefschetz: Differential Equations: Geometric Theory. Interscience Publ., New York, London 1957. | MR | Zbl

[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

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