ON GLOBAL STABILITY IN DISTRIBUTED PARAMETER SYSTEMS

A mehtod is presented for determining finite stability regions for distributed parameter systems whose transient behavior is governed by a single parabolic differential equation. The case of an adiabatic catalytic reaction is discussed in detail. However, the same techniques can be applied to many other systems in which chemical reactions and diffusions are coupled. The method is based on the maximum principle for parabolic partial differential equations. It is shown that finite regions of stability can be determined immediately from the knowledge of the steady state profiles, without having to perform any additional computations. A discussion is included of the case in which the transient behavior is governed by two coupled partial differential equations. © 1968.