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This paper deals with the existence of BV solution for the Euler-Poissonsystem endowed with a $\gamma$ pressure law. More precisely, we prove theexistence of weak solution in the BV framework with arbitrary large initialdata when $\gamma=1+2\epsilon$ satisfies a smallness condition. We use theGlimm scheme combined with a splitting method as introduced in [Poupaud, Rascleand Vila, J. Differential Equations, 1995]. Existence of BV solution of 1-Disentropic 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 ofelectric field, the difficulty arises while controlling the Glimm functionalfor the Euler-Poisson system. It requires a subtle study of wave interaction.In the later part of this article, we discuss the initial-boundary valueproblem for the Euler-Poisson system. We prove the existence of $BV$ solutionfor the initial-boundary value problem with large initial and boundary data. Byan explicit example, we also show ill-posedness of initial-boundary valueproblem for the isentropic Euler equation.

Existence of BV solution for the Euler-Poisson system in one dimension with large initial data