BOUNDEDNESS OF SOLUTIONS OF A CLASS OF INTEGRO-DIFFERENTIAL EQUATIONS IN SEVERAL DIMENSIONS

摘要

A class of linear, integro - differential equations is discussed which includes linearized, time—dependent forms of Boltzmann's equation. Solutions satisfying suitable homogeneous conditions on the boundary of a finite domain in configuration space are shown to depend. boundedly on their initial data and thus, in particular, to be uniquely determined by their initial data.