Abstract
This chapter presents some of the recent work found in mathematics, control systems, and engineering literature on the stability problem for distributed parameter systems. It discusses the space–time reactor kinetics equations, the temperature effects on multiplication, and the simplifications for various feedback models. The chapter also reviews several early stability theorems concerning parabolic partial differential equations. A general in-depth discussion of these techniques and their recent application in obtaining stability criteria for systems of interest is presented in the chapter. In principle, the general stability criteria can be derived by the use of these methods, and it can then be verified if the particular system of interest fits the criteria. In practice, however, it very often happens that the technique has to be applied to the particular system of interest directly because the general criteria are often too severe.
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