  We introduce a one parameter family of non-linear, non-local
integro-differential equations and its limit equation. These equations
originate from a derivation of the linear Boltzmann equation using the
framework of bosonic quantum field theory. We show the existence and uniqueness
of strong global solutions for these equations, and a result of uniform
convergence on every compact interval of the solutions of the one parameter
family towards the solution of the limit equation.
