Abstract
In [7] the existence of weak solutions of a Fokker-Planck-Vlasov equation is proved. In this paper, with a little more stringent assumption we show the uniqueness of weak solutions and establish a criterion of (asymptotic) stability against local disturbations.-As a consequence, in the case of uniqueness the Galerkin method used in [7] is a constructive one, i.e. the whole sequence of all Galerkin-approximations converges.
This work has been supported by Forschungsförderung des Landes Nordrhein-Westfalen.
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References
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Rautmann, R. (1978). On the uniqueness and stability of weak solutions of a fokker-planck-vlasov equation. In: Ansorge, R., Törnig, W. (eds) Numerical Treatment of Differential Equations in Applications. Lecture Notes in Mathematics, vol 679. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067874
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DOI: https://doi.org/10.1007/BFb0067874
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