Steady States Of An Oscillating Polymerization Model

This paper investigates a reaction difusion system under certain initial andboundary conditions of steady states. The system describes an oscillating poly-merization reaction in Chemistry. The main work is as follows: First, we provethe existence of positive solution by constructing parabolic equations of upperand lower solutions, after that we discuss the stability and instability of ellipticequations with constant solutions, on the basis we establish the Turing unstabil-ity. Then, we give a priori estimates of positive solutions of elliptic equations.Finally, the existence and nonexistence of non-constant positive solution are dis-cussed. The main methods used in the research include the method of upper andlower solutions, De Giorgi iteration and Moser iteration, energy estimates and thetheory of topological degree, also some important inequalities.