Stationary solutions of the 1-D Vlasov-Maxwell equations for laser-plasma interaction Mihai Bostan 35A0582D10kinetic equationsVlasov-Maxwell systemweak/mild solutionscharacteristics We study a stationary $1$ D Vlasov-Maxwell system which describes the laser-plasma interaction. Three cases are analyzed~: the classical case, the quasi-relativistic case and the relativistic case. We prove the existence of stationary solution and we establish estimates for the charge and current densities. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.2965 10.1512/iumj.2007.56.2965 en Indiana Univ. Math. J. 56 (2007) 581 - 614 state-of-the-art mathematics http://iumj.org/access/