  This paper deals with the existence of BV solution for the Euler-Poisson
system endowed with a $\gamma$ pressure law. More precisely, we prove the
existence of weak solution in the BV framework with arbitrary large initial
data when $\gamma=1+2\epsilon$ satisfies a smallness condition. We use the
Glimm scheme combined with a splitting method as introduced in [Poupaud, Rascle
and Vila, J. Differential Equations, 1995]. Existence of BV solution of 1-D
isentropic Euler equation for large data and $\gamma=1+2\epsilon$ is proved in
[Nishida and Smoller, Comm. Pure Appl. Math, 1973]. Due to the presence of
electric field, the difficulty arises while controlling the Glimm functional
for the Euler-Poisson system. It requires a subtle study of wave interaction.
In the later part of this article, we discuss the initial-boundary value
problem for the Euler-Poisson system. We prove the existence of $BV$ solution
for the initial-boundary value problem with large initial and boundary data. By
an explicit example, we also show ill-posedness of initial-boundary value
problem for the isentropic Euler equation.
