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Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

Faraj, A. (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40.We consider the stationary one dimensional Schrödinger-Poisson system on a bounded interval with a background potential describing a quantum well. Using a partition function which forces the particles to remain in the quantum well, the limit h®0 in the nonlinear system leads to a uniquely solved nonlinear problem with concentrated particle density. It allows to conclude about the convergence of the solution.

Asymptotic analysis of the initial boundary value problem for the thermoelastic system in a perforated domain

M. Sango (2003)

Colloquium Mathematicae

We study the initial boundary value problem for the system of thermoelasticity in a sequence of perforated cylindrical domains Q T ( s ) , s = 1,2,... We prove that as s → ∞, the solution of the problem converges in appropriate topologies to the solution of a limit initial boundary value problem of the same type but containing some additional terms which are expressed in terms of quantities related to the geometry of Q T ( s ) . We give an explicit construction of that limit problem.

Asymptotic and numerical modelling of flows in fractured porous media

Philippe Angot, Franck Boyer, Florence Hubert (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic length scale, so that we can asymptotically reduce them to immersed polygonal fault interfaces and the model finally consists in a coupling between...

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