Turing Pattern Of A Reaction-difusion Model Of Polymerizations

In this paper, we consider a reaction-difusion system which appears in the modelof polymerizations. First, we prove that the solution to the evolution system is globalexistence. Using Moser’s iteration technique, we give a priori estimates for the corre-sponding stationary system. Second, we study the stability of equilibrium point andfind that the Turing pattern will appear under some conditions. We also establish theresults of existence and non-existence of non-constant positive steady state. In the last,we will show that the bifurcation phenomenon may occur as the parameters are varied.