Existence of solutions and asymtptotic limits of the Euler-Poisson and the quantum drift-diffusion systems [Elektronische Ressource] / Ingrid Violet

Existence of solutions andasymtptotic limitsof the Euler-Poisson and thequantum drift-diffusion systems.Applications to plasmas andsemiconductorsDissertationzur Erlangung des GradesDoktor der Naturwissenschaftenam Fachbereich Physik, Mathematik und Informatikder Johannes Gutenberg-Universit¨at MainzIngrid Violetgeboren in Saint-Etienne (Frankreich)Mainz, 2006AbstractMy work concerns two different systems of equations used in the mathematicalmodeling of semiconductors and plasmas: the Euler-Poisson system and the quan-tumdrift-diffusionsystem. ThefirstisgivenbytheEulerequationsfortheconserva-tion of mass and momentum, with a Poisson equation for the electrostatic potential.The second one takes into account the physical effects due to the smallness of thedevices (quantum effects). It is a simple extension of the classical drift-diffusionmodel which consists of two continuity equations for the charge densities, with aPoisson equation for the electrostatic potential.Using an asymptotic expansion method, we study (in the steady-state case for apotential flow) the limit to zero of the three physical parameters which arise in theEuler-Poisson system: the electron mass, the relaxation time and the Debye length.For each limit, we prove the existence and uniqueness of profiles to the asymptoticexpansion and some error estimates.