Periodic Solutions of the 1D Vlasov-Maxwell System with Boundary Conditions

Mihai Bostan (1)

1 CAIMAN - Scientific computing, modeling and numerical analysis

We study the 1D Vlasov-Maxwell system with time periodic boundary conditions in its classical and relativistic form. For small data we prove existence of weak periodic solutions. It is necessary to impose non vanishing conditions for the incoming velocities in order to control the life-time of particles in the domain. In order to preserve the periodicity, another condition of vanishing the time average of the incoming current is imposed.

Mots clés: MAXWELL EQUATIONS; VLASOV EQUATION; SCHAUDER'S FIXED POINT THEOREM

Domaines: Autre [cs.OH]

Mihai Bostan. Periodic Solutions of the 1D Vlasov-Maxwell System with Boundary Conditions. RR-3554, INRIA. 1998. ⟨inria-00073129⟩