Application of renormalization group techniques to transport in the presence of nonlinear sources and sinks

The paper considers the problem of spreading of a localized distribution due to diffusion in the presence of nonlinear sources and sinks modeling annihilation and creation of material in chemical reactions. The evolution of the parameters characterizing the problem, namely, the amplitude and radius of the distribution, has been investigated under the assumption that the distribution is self-similar. These parameters have been calculated using the renormalization-group method with renormalization of the diffusion coefficient and the total amount of material. As a result, it is possible to classify various regimes of the asymptotic behavior of the system at long times according to the sign of nonlinear interaction constant and the spatial dimensionality. In particular, the conditions under which the regime of asymptotic freedom and the peaking regime are realized have been found. The renormalization group method not only allows us to calculate the exponents of functions with power-law behavior, but also to track the transition to the asymptotic regime and calculate numerical coefficients. Zh. éksp. Teor. Fiz. 115, 1497–1510 (April 1999)