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A rigorous stability result for the Vlasov-Poisson system in three dimensions. (English) Zbl 0791.49030
Summary: It is proven that in a neutral two-component plasma with space homogeneous positively charged background, which is governed by the Vlasov-Poisson system and for which Poisson’s equation is considered on a cube in \({\mathbf R}^ 3\) with periodic boundary conditions, the space homogeneous stationary solutions \(g\) with energy gradient \(\partial g/\partial\varepsilon\leq 0\) and compact support are (nonlinearly) stable in the \(L^ 1\)-norm with respect to weak solutions of the initial value problem.

MSC:
49K40 Sensitivity, stability, well-posedness
49J20 Existence theories for optimal control problems involving partial differential equations
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