GLOBAL-SOLUTIONS TO THE ISOTHERMAL EULER-POISSON SYSTEM WITH ARBITRARILY LARGE DATA

We prove the global existence of a solution to the Euler-Poisson syste m, with arbitrarily large data, in a one-dimensional geometry. The pre ssure law we consider, is deduced from an isothermal assumption for th e electrons gas. In this case, Nishida has already pointed out that th e linear part of the Glimm functional is decreasing with respect to ti me. Using a Glimm scheme, he used this property to construct globally defined weak solutions for the Euler system with arbitrary large data. We follow his outline of proof. Here, a new difficulty arises with th e source term, due to the electric field. A key point is that the Glim m scheme is almost conservative. This quasi-conservation of charge lea ds to a uniform estimate of the total variation of the electric field. This estimate allows to prove the convergence of the scheme. (C) 1995 Academic Press, Inc.