This paper develops a technique for finding Lyapunov functions for the class of nonlinear partial differential equations arising from a reactor system which takes into account the coupling of heat transfer, hydrodynamics, and time-dependent neutron diffusion. As a first step, a generalized Lyapunov function was developed for the linearized reactor system. The result provides the sufficient conditions to system stability (and/or asymptotical stability) with respect to the distributed system parameters. A new Lyapunov function for the nonlinear reactor system was constructed by adding nonlinear terms to that of the linear system. The result enables one to determine the region of stability and indicates the proper feedback function which would insure the global stability of the system.

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