# Seldowitsch equation

The Seldowitsch equation ( Zeldovich equation , after Jakow Borissowitsch Seldowitsch ) is a non-linear partial differential equation of the type of reaction diffusion equation , which is used, for example, to describe combustion processes.

Reaction diffusion equations have the form:

${\ displaystyle \ partial _ {t} u = D \ partial _ {x} ^ {2} u + R (u)}$ where often the concentration of a chemical substance is, the D term describes a diffusion in space and the R term the local (chemical) reactions. In the general case u can also have a vector form and the reactions of several substances are then described. Zeldovich used it to describe combustion, and in this case u stood for temperature. The Zeldovich equation is often given with a in the following form: ${\ displaystyle u}$ ${\ displaystyle R (u)}$ ${\ displaystyle R (u) = u ^ {2} \ cdot (1-u)}$ The work of Zeldovich and David Frank-Kamenezki also provided autowaves (see chemical wave ) as solutions, i.e. self-excited and entertaining waves, as did the simultaneous work of Andrei Kolmogorow ( KPP equation ) and Ronald Fisher .

One variant describes the temporal change in a cluster size distribution during a phase change . It is derived from the cluster dynamic model for homogeneous phase transformation. The rates of growth and shrinkage of clusters of the second phase can be determined via the diffusion, which in turn depends on the free energy (or on the free enthalpy , depending on the boundary conditions). The free energy / enthalpy is usually determined in a similar way to classic nucleation .

## Individual evidence

1. ^ Zeldovich, DA Frank-Kamenezki: Theory of thermal flame propagation (Russian), Journal für Physikalische Chemie, Volume 12, 1938, pp. 100-105, in English translation in Zeldovich, Selected Works, Volume 1, Princeton University Press, 1992, p 262
2. BH Gilding u. a. (Ed.), Traveling waves in nonlinear diffusion-convection equation reaction, Birkhäuser 2004, p. 2
3. F. Haider: Materialphysik I ( Memento of the original from June 25, 2007 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.