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numerical analysis
Using the qualitative theory of differential equations the equivalence of the boundary value and the Cauchy's initial value problem is demonstrated for the slab flat flux reactor. It is found that there exists an interval of the initial (central) fuel concentrations for which the initial value problem (with two algebraic conditions) describes a critical flat flux reactor while solutions outside this interval describe undercritical systems of a nonmultiplying medium.
[1] V. Bartošek, R. Zezula: Flat Flux in a Slab Reactor with Natural Uranium. Journal of Nucl. Energy Pt A/B 20, 129-134, (1966). DOI 10.1016/0368-3230(66)90023-1
[2] E. F. Beckenbach: Modern Mathematics for the Engineer. McGraw-Hill Book Соmр. New York - Toronto - London. Zbl 0098.26402
[3] S. Lefshetz: Differential Equations: Geometric Theory. Interscience Publishers, London 1957. MR 0094488
[4] R. Bellman: Stability Theory of Differential Equations. London 1953. MR 0061235 | Zbl 0053.24705
[5] J. Roček: Private communication, 1966.
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