This work is devoted to the study of a problem resulting from plasma physics: heat transfer of electrons in a plasma close to Maxwellian equilibrium. Firstly, the asymptotic regime of Spitzer-Harm is studied. A model proposed by Schurtz and Nicolai is analyzed and located in the context of hydrodynamic limits outside of the strictly asymptotic. The link to non-local models of Luciani and Mora is established, as well as the mathematical properties such as the principle of maximum and entropy dissipation. Then, a formal derivation from the Vlasov equations is proposed. A hierarchy of intermediate models between the kinetic equations and the hydrodynamic limit is described. In particular, a new system hydrodynamics, integro-differential in nature, is proposed. The system Schurtz and Nicolai appears as a simplification of the system resulting from the diversion. The existence and uniqueness of the solution of the nonstationary system are established in a simplified framework. The last part is devoted to the implementation of a specific numerical scheme for solving these models. We propose a finite volume approach can be effective on unstructured grids. The accuracy of this scheme to capture specific effects such as kinetic, which may not be reproduced by the asymptotic Spitzer-Harm model. The consistency of this pattern with that of the Spitzer-Harm equation is highlighted, paving the way for a strategy of coupling between the two models.
