Boundary value problems for the Vlasov-Maxwell equation in one dimension

Abstract Global existence in time and uniqueness of solutions are proved for the Cauchy problem for the Vlasov-Maxwell system of equations in one dimension. The limiting values of the field ±(x, t) as the space variable x → E ∞ are shown to be uniquely determined by the initial data. This result then yields existence of solutions of various boundary value problems. Solutions periodic in x are also discussed in this same framework.