The model one-dimensional Caushy problem for the Wlasoff equation is considered. The equation describes the slab emission of monochromatic electron flux in the self-consistent electric field. The explicit expression for the electric field is obtained for smooth initial data. This expression is obtained in the Brüman-Lagrange series form. After that the problem of the electron flux determination is reduced to the linear equation of the first order which is solving along characteristics, both in the relativistic and classic cases. At last the sums of written series have been received as functions of Caushy problem’s initial data. So the generalized solutions can be obtained also in terms of such functions with non-smooth initial data as their arguments.

Mathematical modelling in actual problems of science and technics