Diffusion approximation for the linear Boltzmann equation of semiconductor theory with analysis of the initial layer
The author considers the relation between the linear Boltzmann equation and the corresponding hydrodynamic approximation and shows that the latter is the diffusion equation. Two cases are discussed in the consideration of the initial layer when considering the Boltzmann equation for charged particles, one corresponding to a relatively weak external field and the other when the field and the collisions are of the same order of magnitude. A general theory is obtained for the bound of errors in the approximations used, and a condition is developed for the diffusion constant to be positive. There is no illustration of how the abstract ideas considered can be used in any physical situation.
scientific article; zbMATH DE number 1005710
scientific article