Applications in Mathematical Kinetics

Abstract

An important field of applications for the methods we have developed is that of mathematical kinetics. The basic objects of study in this field are the equations of chemical kinetics, and these are nonlinear as a rule. In the simplest but commonly encountered case their right hand sides are algebraic functions, which are formed according to the mechanism of a chemical reaction. Recently, the interest in the nonlinear problems of mathematical kinetics has grown considerably in connection with the vast accumulation of experimental facts revealing critical effects of different kinds (see e.g. [30, 89, 78, 79, 73, 149, 150, 151]). An essential point in the analysis of the appropriate mathematical models is to determine all steady states, i.e. to find all real roots of certain systems of nonlinear algebraic equations in some bounded domain. In connection with the equations of chemical kinetics this problem was considered for the first time in a number of papers [4, 5, 6, 7, 8, 34, 35], which used both traditional approaches as well as methods based on modified elimination procedures for systems of nonlinear algebraic equations [11].