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Asymptotic Analysis - Volume 73, issue 1-2

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Price: EUR 420.00
ISSN 0921-7134 (P)
ISSN 1875-8576 (E)

Impact Factor 2024: 1.1

The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. 

Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.

Asymptotic eigenfunctions for a class of difference operators

Authors: Klein, Markus | Rosenberger, Elke

Article Type: Research Article

Abstract: We analyze a general class of difference operators Hε =Tε +Vε on ℓ2 ((εZ)d ), where Vε is a one-well potential and ε is a small parameter. We construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low lying eigenvalues of Hε . These are obtained from eigenfunctions or quasimodes for the operator Hε , acting on L2 (Rd ), via restriction to the lattice (εZ)d .

Keywords: difference operator, tunneling, WKB-expansion, quasimodes

DOI: 10.3233/ASY-2010-1025

Citation: Asymptotic Analysis, vol. 73, no. 1-2, pp. 1-36, 2011

Price: EUR 27.50

p-Laplacian problems with critical Sobolev exponent

Authors: Palatucci, Giampiero

Article Type: Research Article

Abstract: We use variational methods to study the asymptotic behavior of solutions of p-Laplacian problems with nearly subcritical non-linearity in general, possibly non-smooth, bounded domains.

Keywords: Γ-convergence, concentration, p-Laplacian, critical Sobolev exponent

DOI: 10.3233/ASY-2010-1029

Citation: Asymptotic Analysis, vol. 73, no. 1-2, pp. 37-52, 2011

Price: EUR 27.50

On the Thomas–Fermi ground state in a harmonic potential

Authors: Gallo, Clément | Pelinovsky, Dmitry

Article Type: Research Article

Abstract: We study non-linear ground states of the Gross–Pitaevskii equation in the space of one, two and three dimensions with a radially symmetric harmonic potential. The Thomas–Fermi approximation of ground states on various spatial scales was recently justified using variational methods. We justify here the Thomas–Fermi approximation on an uniform spatial scale using the Painlevé-II equation. In the space of one dimension, these results allow us to characterize the distribution of eigenvalues in the point spectrum of the Schrödinger operator associated with the non-linear ground state.

Keywords: Gross–Pitaevskii equation, Thomas–Fermi, Bose–Einstein, hydrodynamics limit, ground state, Painlevé II

DOI: 10.3233/ASY-2011-1034

Citation: Asymptotic Analysis, vol. 73, no. 1-2, pp. 53-96, 2011

Price: EUR 27.50

Stochastic two-scale convergence of an integral functional

Authors: Sango, Mamadou | Woukeng, Jean Louis

Article Type: Research Article

Abstract: In this paper we discuss the concept of stochastic two-scale convergence, which is appropriate to solve coupled-periodic and stochastic homogenization problems. This concept is a combination of both well-known two-scale convergence and stochastic two-scale convergence in the mean schemes, and is a generalization of the said previous methods. By way of illustration we apply it to solve a homogenization problem related to an integral functional with convex integrand. This problematic relies on the notion of dynamical system which is our basic tool.

Keywords: dynamical system, homogenization, stochastic two-scale convergence

DOI: 10.3233/ASY-2011-1038

Citation: Asymptotic Analysis, vol. 73, no. 1-2, pp. 97-123, 2011

Price: EUR 27.50
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