On singular limits of mean-field equations

• Mean field equations arise as steady state versions of convection-diffusion systems where the convective field is determined as solution of a Poisson equation whose right hand side is affine in the solutions of the convection-diffusion equations. In this paper we consider the repulsive coupling case for a system of 2 convection-diffusion equations. For general diffusivities we prove the existence of a unique solution of the mean field equation by a variational technique. Also we analyse the small-Debye-length limit and prove convergence to either the so-called charge-neutral case or to a double obstacle problem for the limiting potential depending on the data.

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Author: Jean Dolbeault, Peter A. Markowich, Andreas Unterreiter urn:nbn:de:hbz:386-kluedo-10050 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (228) Preprint English 2000 2000 Technische Universität Kaiserslautern 2000/06/21 Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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