Vlasov equation with non‐homogeneous boundary conditions

We study the one‐dimensional Vlasov equation in a rod with non‐homogeneous dissipative and conservative boundary conditions. The study is carried out by means of the theory of semigroups and affine operators. Existence, uniqueness and positivity of the solution are proved. The explicit form of the solution is derived and an approximating sequence is given. Copyright © 2000 John Wiley & Sons, Ltd.