Solvability of an inverse problem for the one-dimensional Boltzmann equation (Q1204697)

The author studies the Boltzmann equation \[ \partial_ tu+v\partial_ xu+\lambda(x,t)\partial_ vu+\mu(x,t)u=f(x,t)g(x,v,t)+Q(u ,u) \] where \(Q\) is the collision integral, \(x\geq 0\), \(v\in\mathbb{R}^ 1\). The inverse problem is to determine the functions \(f,u\) provided the functions \(\lambda\), \(\mu\), \(g\), and \(u|_{x=0}\) are given. The main theorem states that the problem admits a unique analytic solution whenever the given functions satisfy some reasonable conditions.