Asymptotic Analysis - Volume 47, issue 3-4

Authors: Keraani, Sahbi

Article Type: Research Article

Abstract: This paper is dedicated to the semiclassical limit of the nonlinear focusing Schrödinger equation (NLS) with a potential with initial data in the form $Q(\frac{x-x_{0}}{\varepsilon })\,\mathrm{e}^{\mathrm{i}\frac{x\cdot\xi_{0}}{\varepsilon }}$ , where Q is the ground state of the associated unscaled elliptic problem. Using a refined version of the method introduced by Bronski and Jerrard [Math. Res. Lett. 7(2–3) (2000), 329–342], we prove that, up to a time-dependent phase shift, the initial shape is conserved with parameters that are transported by the classical flow.

Keywords: Schrödinger equation, ground state, stability, semiclassical limit, Wigner measure, WKB method

Citation: Asymptotic Analysis, vol. 47, no. 3-4, pp. 171-186, 2006

Authors: Ōuchi, Sunao

Article Type: Research Article

Abstract: Let $\hat{u}(t,x)=\sum_{n=1}^{\infty}u_{n}(x)t^{n},\ (t,x)\in \mathbb{C}\times \mathbb{C}^{d}$ , be a formal power series solution of a nonlinear partial differential equation. We study multisummability of $\hat{u}(t,x)$ . This paper is a continuation of [S. Ōuchi, Multisummability of formal solutions of some linear partial differential equations, J. Differential Equations 185 (2002), 513–549], where linear partial differential equations were treated.

Keywords: asymptotic expansion, formal power series solutions, multisummability

Citation: Asymptotic Analysis, vol. 47, no. 3-4, pp. 187-225, 2006

Authors: Santugini-Repiquet, Kévin

Article Type: Research Article

Abstract: We study the influence of a thin split over the dynamic evolution of a ferromagnetic body. A naive numerical simulation would require a huge number of cells to model the split. To avoid this problem, we introduce an equivalent boundary condition which is obtained by a Taylor expansion in the thickness of the split. We prove the existence of solutions to this new problem and then rigorously establish the convergence of the expansion.

Citation: Asymptotic Analysis, vol. 47, no. 3-4, pp. 227-259, 2006

Authors: Santugini-Repiquet, Kévin

Article Type: Research Article

Abstract: We continue the study of equivalent boundary conditions in ferromagnetic domains crossed by a thin split. In this second part, we add nonhomogeneous boundary conditions arising from interactions such as surface anisotropy and super-exchange. We expand the problem up to the first order and establish equivalent boundary conditions in presence of surface anisotropy and super-exchange. In particular, the well-posedness of the expansion problem with equivalent boundary condition and the convergence in some meaning of the expansion are proven.

Citation: Asymptotic Analysis, vol. 47, no. 3-4, pp. 261-290, 2006

Authors: Boutet de Monvel, Anne | Naboko, Serguei | Silva, Luis O.

Article Type: Research Article

Abstract: We obtain the asymptotic behavior of eigenvalues of Jacobi matrices corresponding to a modified Jaynes–Cummings model with additive and multiplicative modulations using the so-called successive diagonalization method. By comparing the cases with and without modulated entries, we show the influence of periodic modulations on the eigenvalue asymptotics.

Citation: Asymptotic Analysis, vol. 47, no. 3-4, pp. 291-315, 2006

Authors: Scardia, Lucia

Article Type: Research Article

Abstract: The problem of the rigorous derivation of one-dimensional models for nonlinearly elastic curved beams is studied in a variational setting. Considering different scalings of the three-dimensional energy and passing to the limit as the diameter of the beam goes to zero, a nonlinear model for strings and a bending–torsion theory for rods are deduced.

Keywords: dimension reduction, curved beams, nonlinear elasticity

Citation: Asymptotic Analysis, vol. 47, no. 3-4, pp. 317-343, 2006

Article Type: Other

Citation: Asymptotic Analysis, vol. 47, no. 3-4, pp. 345-346, 2006