## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 319-351 |

Number of pages | 33 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 158 |

Issue number | 4 |

DOIs | |

State | Published - Jul 1 2001 |

## ASJC Scopus subject areas

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering