On Singular Limits of Mean-Field Equations
Unterreiter, Andreas; Markowich, Peter; Dolbeault, Jean (2001), On Singular Limits of Mean-Field Equations, Archive for Rational Mechanics and Analysis, 158, 4, p. 319-351. http://dx.doi.org/10.1007/s002050100148
TypeArticle accepté pour publication ou publié
Journal nameArchive for Rational Mechanics and Analysis
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Abstract (EN)Mean-field equations arise as steady state versions of convection-diffusion systems where the convective field is determined by 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 two convection-diffusion equations. For general diffusivities we prove the existence of a unique solution of the mean-field equation by a variational analysis of a saddle point problem (usually without coercivity). Also we analyze 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.
Subjects / KeywordsMean-field equations; convection-diffusion systems; Poisson equation; small-Debye-length limit
Showing items related by title and author.
Dolbeault, Jean; Markowich, Peter; Oelz, Dietmar; Schmeiser, Christian (2007) Article accepté pour publication ou publié