Singular solutions of the Vlasov-Maxwell system on a half line
The Vlasov-Maxwell system describes the time evolution of a collisionless, hot plasma. The electrons or ions are given by a phase-space density which satisfies a first order partial differential equation, the Vlasov equation, and this equation is self-consistently coupled to the Maxwell equations for the electromagnetic field. In order to model physically realistic situations for confined plasmas, the inclusion of boundary conditions for the particles and the fields is very important. In a previous paper the author proved global existence of weak solutions to the corresponding initial-boundary value problem in the three-dimensional case. In the paper under review, he investigates the regularity of solutions for a plasma on a half line; in such a one-dimensional situation the system reduces to the Vlasov-Poisson system. The boundary conditions considered include purely specular reflection as well as partial absorption of the particles, and the detailed and comprehensive analysis reveals that the regularity or singularity of the solutions depends strongly on the type of boundary conditions and on whether the plasma is monocharged, contains differently charged particles, or is neutral. For example, in the case of partial absorption and two oppositely charged particle species, examples show that singularities appear at the boundary and propagate along characteristics into the plasma.
scientific article; zbMATH DE number 832138