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Cauchy problem; time dependent; nonlinear transport; initial value problem; reactor kinetics with temperature feedback; Local and Global existence; uniqueness; analytical solution; neutron flux
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.
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