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Keywords:
Cauchy problem; time dependent; nonlinear transport; initial value problem; reactor kinetics with temperature feedback; Local and Global existence; uniqueness; analytical solution; neutron flux
Cauchy problem; time dependent; nonlinear transport; initial value problem; reactor kinetics with temperature feedback; Local and Global existence; uniqueness; analytical solution; neutron flux
Summary:
In this paper, the initial value problem for the equations of reactor kinetics is solved and the temperature feedback is taken into account. The space where the problem is solved is chosen in such a way that it may correspond best of all to the mathematical properties of the cross-section models. The local solution is found by the method of iterations, its uniqueness is proved and it is shown also that existence of global solution is ensured in the most cases. Finally, the problem of mild solution is discussed.
References:
[1] J. Mika D. Obradovič R. Stankiewicz: Spectral properties of a multigroup transport operator with delayed neutrons in plane geometry. Bulletin of the Boris Kidrič Institute of Nuclear Sciences, Vol. 19, Nuclear engineering, No. 5, P/433 (1968).
[2] Ю. И. Ершов С. Б. Шихов: Математические основы теории переноса. том 2, Москва (1985). Zbl 1223.81132
[3] P. F. Zweifel: Reactor Physics. New York (1973).
[4] J. Kyncl: Initial value problem for the equations of reactor kinetics. ÚJV 8021-R (1987).
[5] A. Friedman: Partial differential equations of parabolic type. Prentice-Hall, inc., Engelwood Cliffs, N.J. (1964). MR 0181836 | Zbl 0144.34903
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