The Global Dynamics of Isothermal Chemical Systems with Critical Nonlinearity

In this paper, we study the Cauchy problem of a cubic autocatalytic chemical reaction system u1,t = u1,xx − u1u β 2 , u2,t = du2,xx + u α 1u β 2 with non-negative initial data, where the exponents α, β satisfy 1 < α, β < 2, α+ β = 3 and the constant d > 0 is the Lewis number. Our purpose is to study the global dynamics of solutions under mild decay of initial data as |x| → ∞. We show the exact large time behaviour of solutions which is universal.