The global self-similarity of a chemical reaction system with critical nonlinearity
Abbreviated Journal Title
Proc. R. Soc. Edinb. Sect. A-Math.
UNEQUAL DIFFUSION RATES; FORM TRAVELING-WAVES; CUBIC AUTOCATALYSIS; ORDER AUTOCATALYSIS; COMBUSTION SYSTEM; MODEL; Mathematics, Applied; Mathematics
In this paper, we study the Cauchy problem of a cubic autocatalytic chemical reaction system u(1,t)=u(1,xx) - u(1)u(2)(2), u(2,t)=du(2,xx)+u(1)u(2)(2) with non-negative initial data, where 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 vertical bar x vertical bar -> infinity. In particular, we show that, for a substantial class of L-1 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.
Proceedings of the Royal Society of Edinburgh Section a-Mathematics
"The global self-similarity of a chemical reaction system with critical nonlinearity" (2007). Faculty Bibliography 2000s. 7542.