Asymptotic Analysis - Volume 28, issue 1

Authors: Lods, Véronique | Mardare, Cristinel

Article Type: Research Article

Abstract: We estimate the difference between the solutions of the three‐dimensional model and the two‐dimensional Naghdi model for a thin shell. This estimation, which depends on the thickness of the shell, is obtained under the assumption that the shell is clamped along its entire lateral face.

Citation: Asymptotic Analysis, vol. 28, no. 1, pp. 1-30, 2001

Authors: Han, Jongmin

Article Type: Research Article

Abstract: In this paper we study asymptotic behaviors of the maximal vortex condensate solutions in the Chern–Simons–Higgs theory when the coupling parameter κ goes to zero. Using Tarantello's weak convergence result for F12 [16], we derive the weak convergence of A0 /κ. As a consequence we compute the locally uniform convergence rate of Higgs fields, |�κ |2 →1, away from the vortices and the blow‐up rate of |ψκ j |2 at the vortex point pj .

Citation: Asymptotic Analysis, vol. 28, no. 1, pp. 31-48, 2001

Authors: Jüngel, Ansgar | Peng, Yue‐Jun

Article Type: Research Article

Abstract: This paper is a continuation of a series of papers in which (quasi‐) hydrodynamic models for plasmas are rigorously derived by means of asymptotic analysis. Here, the quasi‐neutral limit (zero‐Debye‐length limit) in the drift‐diffusion equations is performed in the two cases: weakly ionized plasmas and not weakly ionized plasmas. The model consists of the continuity equations for the electrons and ions, the constitutive relations for the particle current densities, and the Poisson equation for the electrostatic potential in a bounded domain. In the case of a weakly ionized plasma, the continuity equation for the electrons is replaced by a …relation between the electrostatic potential and the electron density such that the Poisson equation becomes nonlinear. The equations are complemented by mixed Dirichlet–Neumann boundary conditions and initial conditions. The quasi‐neutral limits are shown without assuming compatibility conditions on the boundary densities. The proofs rely on the use of the so‐called entropy functional which yields appropriate uniform estimates, and compensated compactness methods. Show more

Keywords: asymptotic analysis, singular perturbation, drift‐diffusion equations, plasmas, entropy method, boundary layers

Citation: Asymptotic Analysis, vol. 28, no. 1, pp. 49-73, 2001

Authors: Guarguaglini, F.R. | Terracina, A.

Article Type: Research Article

Abstract: We present a relaxation semilinear system of conservation laws with source which approximates nonlinear parabolic equations with initial and boundary conditions. The system can be interpreted as a BGK (Bhatnagar, Gross, Krook) model with a finite number of velocities. We prove the well‐posedness of the model, a priori estimates and we obtain the convergence towards the solution of the parabolic problem. Moreover we prove a similar result for a weakly degenerate problem.

Keywords: parabolic nonlinear conservation laws, degenerate parabolic equations, singular perturbation problems, BGK models

Citation: Asymptotic Analysis, vol. 28, no. 1, pp. 75-89, 2001