On Semigroup Theory and Its Application to Space-Time Nuclear Reactor Dynamics

The methods of semigroup theory are extended and applied to the space-time reactor dynamics equations. The extension allows one to obtain an upper bound on the maximum value of the state variables as well as a stability criteria based on the L_∞ norm. Several important questions relating to obtaining bounds on the linear operators of reactor theory are answered. The importance of considering the L_∞ or max norm is discussed and the main results are applied to an illustrative example.