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PrefaceIn recent years considerable interest has developed in the mathematical analysis of chemically reacting systems both in the absence and in the presence of diffusion. Earlier work has been limited to simple problems amenable to closed form solutions, but now the computer permits the numerical solution of complex systems of nonlinear differential equations. The numerical approach provides quantitative information, but for practical reasons it must be limited to a rather narrow range of the parameters of the problem. Consequently, it is desirable to obtain broader qualitative information about the solutions by investigating from a more fundamental mathematical point of view the structure of the differential equations. This theoretical approach can actually complement and guide the computational approach by narrowing down trial and error procedures, pinpointing singularities and suggesting methods for handling them. The study of the structure of the differential equations may also clarify some physical principles and suggest new experiments. A serious limitation ofthe theoretical approach is that many of the results obtained, such as the sufficient conditions for the stability of the steady state, turn out to be very conservative. Thus the theoretical and computational approaches are best used together for the purpose of understanding, designing, and controlling chemically reacting systems.The present monograph is intended as a contribution to the theory of the differential equations describing chemically reacting systems. The main topics treated are the a priori bounds and the existence of solutions, the conditions for uniqueness and stability of solutions and the asymptotic behavior of solutions. Most of these problems have been treated by using methods from nonlinear functional analysis and especially fixed point methods. The closely related theory of bifurcation points seems to hold promise for further progress.It is hoped that the monograph will be of interest to both the theoretical engineer and the applied mathematician. The former will notice that chemical reactions have been considered in the framework of three specific systems, the uniform isolated system (batch reactor), a uniform open system (stirred-tank reactor), and a distributed system (catalyst pellet). However, most of the methods presented should be useful in analyzing other systems such as fixed bed reactors. The complex systems VIII Preface of biological reactions seem also to offer an exciting ground for mathematical analysis. The applied mathematician will hopefully find an element of elegance and generality in the differential equations of chemical systems. These equations seem to be an ideal subject for the application and further development of nonlinear analysis.I have tried to cite references with the latest information on each subject discussed and have not attempted to reference the earliest contributors. Consequently, I have emphasized recent papers and textbooks which in tum give access to the earlier work.I am indebted to Profe...