Asymptotic Analysis - Volume 27, issue 3-4

Authors: Palmeri, Maria Carla

Article Type: Research Article

Citation: Asymptotic Analysis, vol. 27, no. 3-4, pp. 185-194, 2001

Authors: Butler, J.

Article Type: Research Article

Abstract: We obtain a new two‐term asymptotic formula for the counting function of eigenvalues of h pseudodifferential operators in the limit as h→0. Recent results concerning clustering of eigenvalues obtained in [7] follow in corollary and, as an application, we consider the semi‐classical behaviour of the quantum current studied recently in [2].

Citation: Asymptotic Analysis, vol. 27, no. 3-4, pp. 195-218, 2001

Authors: Fedotov, Alexander | Klopp, Frédéric

Article Type: Research Article

Abstract: This work is devoted to a new version of the complex WKB method suited for adiabatic perturbations of one‐dimensional periodic Schrödinger operators. Therefore, we introduce an additional parameter, and it is this parameter (and not the variable of the equation) that will become complex. This naturally leads to canonical domains where we construct solutions of the Schrödinger equation with a standard asymptotic behavior. These can be used to compute the asymptotics of the exponentially small coefficients of transfer matrices (e.g., scattering matrices, monodromy matrices, etc.). We give an example of such a computation. Résumé. Ce travail est consacré à …une nouvelle version de la méthode BKW complexe adaptée à l'étude des perturbations adiabatiques d'équations de Schrödinger périodiques en dimension 1. Nous introduisons un paramètre supplémentaire; c'est ce paramètre qui sera rendu complexe (au lieu de la variable de l'équation). Ceci nous conduit de façon naturelle à la définition des domaines canoniques dans lesquels on construit des solutions aux comportements asymptotiques connus. Ces développements asymptotiques peuvent être utilisés pour contrôler l'asymptotique des coefficients exponentiellement petits de matrices de transfert (par exemple, de matrices de diffusion, de matrices de monodromie, etc.). On donne un exemple d'un tel calcul. Show more

Keywords: periodic Schrödinger equation, adiabatic perturbations, complex WKB method

Citation: Asymptotic Analysis, vol. 27, no. 3-4, pp. 219-264, 2001

Authors: Quintanilla, R.

Article Type: Research Article

Abstract: This paper derives spatial decay bounds in a dynamical problem of incremental thermoelasticity defined on a semi‐infinite cylindrical region. Previous results for isothermal elastodynamics and the parabolic heat equation lead us to suspect that the solution of the problem should tend to zero faster than a decaying exponential of the distance from the finite end of the cylinder. We prove that an energy expression is actually bounded above by a decaying exponential of a quadratic polynomial of the distance. As it has been previously proved for usual linear thermoelasticity, this is reminiscent of the decay rate in second order parabolic …problems. Show more

Keywords: incremental thermoelastodynamics, spatial estimates, Saint‐Venant's principle

Citation: Asymptotic Analysis, vol. 27, no. 3-4, pp. 265-279, 2001

Authors: Knessl, Charles | Yang, Yongzhi (Peter)

Article Type: Research Article

Abstract: We consider a Brownian particle that is subject to (1) a time‐dependent convection (or drift) field and (2) a reflecting barrier. We let Y(T) be the particle's position at time T. There is a standard reflecting barrier that constrains the particle to the non‐negative real axis (i.e., Y(T)≥0). We assume that Y(T0 )=X0 ≥0 with probability one, and that the drift field is linearly dependent upon time. Specifically, we assume that the drift changes sign at T=0 and becomes positive for T>0. Such models arise naturally in several areas, including convection–diffusion problems in mathematical physics and the study of time …dependent queues. We obtain an exact expression for the probability density Q, with Q(X,T) dX=Prob[Y(T)∈(X,X+ dX)|Y(T0 )=X0 ≥0], in terms of Airy functions. We then obtain detailed asymptotic results, that apply for X0 and/or T0 →∞, and various ranges of the space–time (X,T) plane. We interpret our results in terms of semi‐classical mechanics. Show more

Citation: Asymptotic Analysis, vol. 27, no. 3-4, pp. 281-319, 2001

Authors: Volkmer, Hans

Article Type: Research Article

Abstract: Using the Darboux method of asymptotic analysis, it is shown that the coefficients of the power series expansions of the functions f(w)=(1−w)−c (1−2xw+w2 )−c and (1+w)f(w), 1<c<2, at w=0 are positive if x lies in certain intervals. This partially answers some questions raised by Askey.

Citation: Asymptotic Analysis, vol. 27, no. 3-4, pp. 321-334, 2001

Authors: Muñoz Rivera, Jaime E. | Perla Menzala, Gustavo

Article Type: Research Article

Abstract: In this paper we consider the dynamical full von Kármán system of equations for viscoelastic plates. The main result of this paper says that the uniform rate of decay of the energy function associated with the system depends on the rate of decay of the relaxation functions. Our result can be seem as a refinement of our previous work [23] on the so called “modified” von Kármán model in which case the in‐plane displacements are not taken into account.

Keywords: viscoelasticity, exponential decay, initial boundary value problem

Citation: Asymptotic Analysis, vol. 27, no. 3-4, pp. 335-357, 2001

Article Type: Other

Citation: Asymptotic Analysis, vol. 27, no. 3-4, pp. 359-359, 2001

Article Type: Other

Citation: Asymptotic Analysis, vol. 27, no. 3-4, pp. 361-361, 2001