ANALYSIS OF AN OPERATOR EQUATION WITH THE DIFFERENTIABLE IN BANACH SPACE OPERATOR AND ITS APPLICATION TO THE INVESTIGATION OF REACTOR MODEL DYNAMICS

Michał Podowski

Abstract


An operator equation of the following form
λx = z + F(x),
where z - an element of Banach space X and F(x)∈X for x∈D⊂X, is investigated. In the cas of m-order differentiable operator F (m>3), conditions of existence and uniqueness of a solution of considered equation are formulated and an estimation of the norm of this solution as a function of the norm z is obtained.

The results of theoretical analysis are applied to the point reactor model with nonlinear, temperature-type reactivity feedback. The conditions of the asymptotic stability for the autonomous system as well as for the system including the external reactivity oscilations, are formulated.


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