Asymptotic Analysis - Volume 55, issue 3-4

Authors: Chipot, Michel

Article Type: Research Article

Abstract: We investigate the asymptotic behavior of some anisotropic diffusion problems and give some estimates on the rate of convergence of the solution toward its limit. We also relate this type of elliptic problems to problems set in cylinder becoming unbounded in some directions and show how some information on one type leads to information for the other type and conversely.

Citation: Asymptotic Analysis, vol. 55, no. 3-4, pp. 125-144, 2007

Authors: Kachmar, Ayman

Article Type: Research Article

Abstract: We formulate a spectral problem related to the onset of superconductivity for a generalized Ginzburg–Landau model, where the order parameter and the magnetic potential are defined in the whole space. This model is devoted to the ‘proximity effect’ for a superconducting sample surrounded by a normal material. In the regime when the Ginzburg–Landau parameter (of the superconducting material) is large, we estimate the critical applied magnetic field for which the normal state will lose its stability, a result that has some roots in the physical literature. In some asymptotic situations, we recover results related to the ‘standard’ Ginzburg–Landau model, where …we mention in particular the two-term expansion for the upper critical field obtained by Helffer–Pan. Show more

Keywords: generalized Ginzburg–Landau equations, proximity effects, Schrödinger operator with magnetic field, semiclassical analysis

Citation: Asymptotic Analysis, vol. 55, no. 3-4, pp. 145-201, 2007

Authors: Sourisse, Arnaud | Wang, Xue Ping

Article Type: Research Article

Abstract: On étudie l'asymptotique des valeurs propres de l'opérateur de Dirac en dimension deux avec un champ magnétique variable qui tend vers l'infini. On utilise la structure supersymétique de cet opérateur pour se ramener à l'étude des valeurs propres de l'opérateur de Schrödinger avec un potentiel électrique égal au champ magnétique.

Keywords: opérateur de Dirac, champ magnétique, valeur propre

Citation: Asymptotic Analysis, vol. 55, no. 3-4, pp. 203-228, 2007

Authors: Shang, Chanyu

Article Type: Research Article

Abstract: This paper deals with the one-dimensional nonlinear thermoviscoelastic system subject to constant temperature boundary conditions, describing phase transitions in shape memory alloys. We shall prove the global existence and uniqueness of the weak solution for initial data (strain, velocity, absolute temperature) (u0 , v0 , θ0 )∈L∞ ×W0 1,∞ ×H1 . Furthermore, we investigate the asymptotic behavior as time tends to infinity and establish the following asymptotic properties for the weak solution: As t→∞, v→0 in H1 (0, 1), θ→T0  in L∞ (0, 1), u(x, t)→u∞ (x) a.e., where u∞ ∈L∞ is a stationary state satisfying …f1 (u∞ )T0 +f2 (u∞ )=0, a.e., in [0, 1]. Here we work in a framework in which u belongs to L∞ to describe phase transitions between different configurations of crystal lattices. Show more

Keywords: shape memory alloys, asymptotic behavior, phase transitions

Citation: Asymptotic Analysis, vol. 55, no. 3-4, pp. 229-251, 2007

Article Type: Other

Citation: Asymptotic Analysis, vol. 55, no. 3-4, pp. 253-253, 2007