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Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations

Yue-Jun Peng (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We deal with boundary layers and quasi-neutral limits in the drift-diffusion equations. We first show that this limit is unique and determined by a system of two decoupled equations with given initial and boundary conditions. Then we establish the boundary layer equations and prove the existence and uniqueness of solutions with exponential decay. This yields a globally strong convergence (with respect to the domain) of the sequence of solutions and an optimal convergence rate O ( ε 1 2 ) to the quasi-neutral...

Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations

Yue-Jun Peng (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We deal with boundary layers and quasi-neutral limits in the drift-diffusion equations. We first show that this limit is unique and determined by a system of two decoupled equations with given initial and boundary conditions. Then we establish the boundary layer equations and prove the existence and uniqueness of solutions with exponential decay. This yields a globally strong convergence (with respect to the domain) of the sequence of solutions and an optimal convergence rate O ( ε 1 2 ) to the quasi-neutral...

Boundary layer correctors and generalized polarization tensor for periodic rough thin layers. A review for the conductivity problem

Clair Poignard (2012)

ESAIM: Proceedings

We study the behaviour of the steady-state voltage potential in a material composed of a two-dimensional object surrounded by a rough thin layer and embedded in an ambient medium. The roughness of the layer is supposed to be εα–periodic, ε being the magnitude of the mean thickness of the layer, and α a positive parameter describing the degree of roughness. For ε tending to zero, we determine the appropriate boundary layer correctors which lead to approximate transmission conditions equivalent to...

Boundary layer for Chaffee-Infante type equation

Roger Temam, Xiaoming Wang (1998)

Archivum Mathematicum

This article is concerned with the nonlinear singular perturbation problem due to small diffusivity in nonlinear evolution equations of Chaffee-Infante type. The boundary layer appearing at the boundary of the domain is fully described by a corrector which is “explicitly" constructed. This corrector allows us to obtain convergence in Sobolev spaces up to the boundary.

Boundary layer tails in periodic homogenization

Grégoire Allaire, Micol Amar (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper focus on the properties of boundary layers in periodic homogenization in rectangular domains which are either fixed or have an oscillating boundary. Such boundary layers are highly oscillating near the boundary and decay exponentially fast in the interior to a non-zero limit that we call boundary layer tail. The influence of these boundary layer tails on interior error estimates is emphasized. They mainly have two effects (at first order with respect to the period ε): first, they add...

Boundary observability for the space semi-discretizations of the 1 – d wave equation

Juan Antonio Infante, Enrique Zuazua (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider space semi-discretizations of the 1-d wave equation in a bounded interval with homogeneous Dirichlet boundary conditions. We analyze the problem of boundary observability, i.e., the problem of whether the total energy of solutions can be estimated uniformly in terms of the energy concentrated on the boundary as the net-spacing h → 0. We prove that, due to the spurious modes that the numerical scheme introduces at high frequencies, there is no such a uniform bound. We prove however a...

Boundary regularity and compactness for overdetermined problems

Ivan Blank, Henrik Shahgholian (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let D be either the unit ball B 1 ( 0 ) or the half ball B 1 + ( 0 ) , let f be a strictly positive and continuous function, and let u and Ω ⊂ D solve the following overdetermined problem: Δ u ( x ) = χ Ω ( x ) f ( x ) in D , 0 ∈ ∂ Ω , u = | ∇ u | = 0 in Ω c , where χ Ω denotes the characteristic function of Ω , Ω c denotes the set D ∖ Ω , and the equation is satisfied in the...

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