A toy model for resonant transport (Q2837182)

The author presents analysis to some toy models describing the motion of charged particles in the electro-magnetic field (Vlasov-Maxwell model). For the general model, the question of global in time existence of solutions is open, except some special cases. It is connected with the possibility that the particles may almost achieve the speed of the light.NEWLINENEWLINEFor an easy toy model in 1D, the author proves existence and uniquencess of classical solutions. The proof is based on suitable a-priori estimates.NEWLINENEWLINENext, he considers a more complex problem (still in 1D) to which he proves existence of a solution on finite time interval and characterizes the possible blow up time in different situations.