On the 1-dimensional model problem for the Wlasoff equation. Part I

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. 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.