The Vlasov–Poisson system models a collisionless plasma. In a bounded domain it is known that singularities can occur. Existence of global in time continuous solutions to the Vlasov–Poisson system is proven in a one-dimensional bounded domain, with direct reflection boundary conditions and initial data even with respect to the -variable. Local in time uniqueness is proven. Generalized characteristics are used. Electroneutrality is obtained in the limit.
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