The global self-similarity of a chemical reaction system with critical nonlinearity

Abstract

In this paper, we study the Cauchy problem of a cubic autocatalytic chemical reaction system u_{1,t}=u_{1,xx}-u_1u^{2}_2,\qquad u_{2,t}=du_{2,xx}+u_1u^{2}_2 initial data, the exact large-time behaviour of solutions is characterized by a universal, non-Gaussian spatio-temporal profile, subject to the apparent conservation of total mass.