Asymptotic Analysis - Volume 63, issue 4

Authors: de Bouard, Anne | Fukuizumi, Reika

Article Type: Research Article

Abstract: We study the asymptotic behavior of the solution of a model equation for Bose–Einstein condensation, in the case where the trapping potential varies randomly in time. The model is the so called Gross–Pitaevskii equation, with a quadratic potential with white noise fluctuations in time whose amplitude ε tends to zero. The initial condition of the solution is a standing wave solution of the unperturbed equation. We prove that up to times of the order of ε−2 , the solution decomposes into the sum of a randomly modulated standing wave and a small remainder, and we derive the equations for the …modulation parameters. In addition, we show that the first order of the remainder, as ε goes to zero, converges to a Gaussian process, whose expected mode amplitudes concentrate on the third eigenmode generated by the Hermite functions, on a certain time scale. Show more

Keywords: nonlinear Schrödinger equation, stochastic partial differential equations, white noise, harmonic potential, standing waves, expected mode powers

DOI: 10.3233/ASY-2008-0931

Citation: Asymptotic Analysis, vol. 63, no. 4, pp. 189-235, 2009

Authors: Bartczak, Leszek

Article Type: Research Article

Abstract: We study the asymptotic behaviour of the solution to coercive models of inelastic deformation with damping. We look for conditions on the boundary data, the external force and the nonlinearity such that the solution of our problem converges to a stationary solution.

Keywords: viscoplasticity, materials with memory, nonlinear constitutive equations, deformations with damping, asymptotic analysis

DOI: 10.3233/ASY-2009-0938

Citation: Asymptotic Analysis, vol. 63, no. 4, pp. 237-252, 2009

Article Type: Other

Citation: Asymptotic Analysis, vol. 63, no. 4, pp. 253-253, 2009