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Asymptotic Analysis - Volume 76, issue 1

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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.

A simplified model for elastic thin shells

Authors: Blanchard, Dominique | Griso, Georges

Article Type: Research Article

Abstract: We introduce a simplified model for the minimization of the elastic energy in thin shells. This model is not obtained by an asymptotic analysis. The nonlinear simplified model admits always minimizers by contrast with the original one. We show the relevance of our approach by proving that the rescaled minimum of the simplified model and the rescaled infimum of the full model have the same limit as the thickness tends to 0. The simplified energy can be expressed as a functional acting over fields defined on the mid-surface of the shell and where the thickness remains as a parameter.

Keywords: nonlinear elasticity, shells

DOI: 10.3233/ASY-2011-1057

Citation: Asymptotic Analysis, vol. 76, no. 1, pp. 1-33, 2012

Price: EUR 27.50

Interface dynamics of the porous medium equation with a bistable reaction term

Authors: Alfaro, Matthieu | Hilhorst, Danielle

Article Type: Research Article

Abstract: We consider a degenerate partial differential equation arising in population dynamics, namely the porous medium equation with a bistable reaction term. We study its asymptotic behavior as a small parameter, related to the thickness of a diffuse interface, tends to zero. We prove the rapid formation of transition layers which then propagate. We prove the convergence to a sharp interface limit whose normal velocity, at each point, is that of the underlying degenerate travelling wave.

Keywords: degenerate diffusion, singular perturbation, sharp interface limit, population dynamics

DOI: 10.3233/ASY-2011-1067

Citation: Asymptotic Analysis, vol. 76, no. 1, pp. 35-48, 2012

Price: EUR 27.50

The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions

Authors: Borisov, Denis | Krejčiřík, David

Article Type: Research Article

Abstract: The Laplacian in an unbounded tubular neighbourhood of a hyperplane with non-Hermitian complex-symmetric Robin-type boundary conditions is investigated in the limit when the width of the neighbourhood diminishes. We show that the Laplacian converges in a norm resolvent sense to a self-adjoint Schrödinger operator in the hyperplane whose potential is expressed solely in terms of the boundary coupling function. As a consequence, we are able to explain some peculiar spectral properties of the non-Hermitian Laplacian by known results for Schrödinger operators.

Keywords: Laplacian in shrinking tubular neighbourhoods, non-Hermitian Robin boundary conditions, effective Hamiltonian, PT-symmetry, J-self-adjointness, norm-resolvent convergence

DOI: 10.3233/ASY-2011-1061

Citation: Asymptotic Analysis, vol. 76, no. 1, pp. 49-59, 2012

Price: EUR 27.50
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