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Author: Glitzky, Annegret × End date: 2009 × Start date: 2000 × Has files: Yes × Type: Text × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: existence ×

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Now showing 1 - 5 of 5
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    Resolvent estimates in W-1,p related to strongly coupled linear parabolic systems with coupled nonsmooth capacities
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Glitzky, Annegret; Hünlich, Rolf
    We investigate linear parabolic systems with coupled nonsmooth capacities and mixed boundary conditions. We prove generalized resolvent estimates in W-1,p spaces. The method is an appropriate modification of a technique introduced by Agmon to obtain Lp estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result.
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    Stationary solutions to an energy model for semiconductor devices where the equations are defined on different domains
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Glitzky, Annegret; Hünlich, Rolf
    We discuss a stationary energy model from semiconductor modelling. We accept the more realistic assumption that the continuity equations for electrons and holes have to be considered only in a subdomain $Omega_0$ of the domain of definition $Omega$ of the energy balance equation and of the Poisson equation. Here $Omega_0$ corresponds to the region of semiconducting material, $OmegasetminusOmega_0$ represents passive layers. Metals serving as contacts are modelled by Dirichlet boundary conditions. We prove a local existence and uniqueness result for the two-dimensional stationary energy model. For this purpose we derive a $W^1,p$-regularity result for solutions of systems of elliptic equations with different regions of definition and use the Implicit Function Theorem.
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    Analysis of a spin-polarized drift-diffusion model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Glitzky, Annegret
    We introduce a spin-polarized drift-diffusion model for semiconductor spintronic devices. This coupled system of continuity equations and a Poisson equation with mixed boundary conditions in all equations has to be considered in heterostructures. We give a weak formulation of this problem and prove an existence and uniqueness result for the instationary problem. If the boundary data is compatible with thermodynamic equilibrium the free energy along the solution decays monotonously and exponentially to its equilibrium value. In other cases it may be increasing but we estimate its growth. Moreover we give upper and lower estimates for the solution.
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    Existence of bounded steady state solutions to spin-polarized drift-diffusion systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Glitzky, Annegret; Gärtner, Klaus
    We study a stationary spin-polarized drift-diffusion model for semiconductor spintronic devices. This coupled system of continuity equations and a Poisson equation with mixed boundary conditions in all equations has to be considered in heterostructures. In 3D we prove the existence and boundedness of steady states. If the Dirichlet conditions are compatible or nearly compatible with thermodynamic equilibrium the solution is unique. The same properties are obtained for a space discretized version of the problem: Using a Scharfetter-Gummel scheme on 3D boundary conforming Delaunay grids we show existence, boundedness and, for small applied voltages, the uniqueness of the discrete solution.
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    Electro-reaction-diffusion systems in heterostructures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2000) Glitzky, Annegret; Hünlich, Rolf
    The paper is devoted to the mathematical investigation of a general class of electro-reaction-diffusion systems with nonsmooth data which arises in applications to semiconductor technology. Besides of a basic problem, a reduced problem is considered which is obtained if the kinetics of the free carriers is fast. For two dimensional domains we prove a global existence and uniqueness result. In addition, asymptotic properties of solutions are studied. Basic ideas are energy estimates, Moser iteration, regularization techniques and an existence result for electro-diffusion systems with weakly nonlinear volume and boundary source terms which is proved in the paper, too. The relationship between the property that the energy functional decays exponentially in time to its equilibrium value and the existence of global positive lower bounds for the densities of the species is investigated. We illustrate relations between the model and its reduced version in general and for concrete examples. Finally, we discuss the special features of heterostructures for simplified model problems.