ABOUT SMOOTHNESS OF THE SOLUTION OF SOME INVERSE PROBLEM FOR MAXWELL-BOLTZMANN EQUATION

Abstract

Proved differentiability of weak solution of inverse problem for Maxwell-Boltzmann equation which describes the distribution of electronic component discharged plasma in bounded domain of three-dimensional space. This inverse problem is investigated in terms of abstract differential equations in a Banach spaces from the viewpoint of semigroup theory. The task of determining the source function reduces to an integral equation of Voltera of the second kind. This equation is extended to a system of equations with an equation with the derivative. The study of this system allows us to obtain the condition of differentiability of the inverse problem for the original MaxwellBoltzmann’s equation.