Existence, uniqueness and properties of the solutions of the Boltzmann kinetic equation for a weakly ionized gas. I.

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Abstract
The Boltzmann kinetic equation for a weakly ionized gas in the presence of a time dependent exterior electric field and a static exterior magnetic field has been transformed into an integral equation. Existence and uniqueness theorems have been proved for inverse power‐law potentials of the form A/rs with s≳3 and for a large class of initial distribution functions. For soft potentials (3<s⩽5), these theorems have been derived from the general properries of the integral operator. For hard potentials, 5<s⩽+∞, where no generla properties of the integral operator can be directly proved, an iteration procedure which constitutes the main part of the present work has been developed. In each case, some important properties of the solution have been established.

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