SINGULAR PERTURBATION PROBLEM FOR AN ENVE LOPE EQUATION IN PLASMA PHYSICS

We investigate the Langmuir wave envelope approximation which consists in taking the limit omega --> infinity in the nonlinear plasma wave e quation [GRAPHICS] We prove that the local-in-time Cauchy problem for this equation is well-posed in H-2 x H-1. We construct solutions that blow up in a finite time. We show that when omega --> infinity, E(o)me ga converges to the solution of the limit equation, and we finally com pare the existence times of E(o)mega and of its limit when omega --> i nfinity.