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Asymptotic Analysis - Volume 61, 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.

Multi-materials with strong interface: Variational modelings

Authors: Bessoud, Anne Laure | Krasucki, Françoise | Michaille, Gérard

Article Type: Research Article

Abstract: We introduce a simplified model for a multi-material made up of two elastic bodies connected by a strong thin material layer whose stiffness grows as 1/ε. The model is obtained by identifying the Γ-limit of the stored strain energy functional of the physical problem when the thickness ε of the intermediate layer tends to zero. The intermediate layer behaves as a stiffening elastic membrane. Furthermore, in the linear anisotropic case, we establish the strong convergence of the exact solution toward the solution of the limit problem.

Keywords: elasticity, multi-materials, multi-scaling, Γ-convergence

DOI: 10.3233/ASY-2008-0903

Citation: Asymptotic Analysis, vol. 61, no. 1, pp. 1-19, 2009

Price: EUR 27.50

An averaging principle for moment equations of branching diffusion processes with fast transformation rate

Authors: Chen, Zhiwei | Molchanov, Stanislav

Article Type: Research Article

Abstract: A multi-type branching diffusion process with fast transmutations between particles are considered in this paper. The first moment equations for the process are reaction–diffusion equations. As the inverse transmutation rate approaches 0, we derive an averaging principle for these reaction–diffusion equations.

Keywords: branching diffusion process, averaging principle, reaction–diffusion equation

DOI: 10.3233/ASY-2008-0913

Citation: Asymptotic Analysis, vol. 61, no. 1, pp. 21-34, 2009

Price: EUR 27.50

Stability property of the two-dimensional Keller–Segel model

Authors: Raczyński, Andrzej

Article Type: Research Article

Abstract: The paper contains results concerning the stability properties of solutions to a simplified Keller–Segel problem modelling chemotaxis in the whole space R2 . First, the existence of solutions to considered system is proved, as well as for this system with the elliptic equation replaced by its parabolic version with time derivative multiplied by a positive parameter ε. Secondly, the stability of the model is shown, namely the convergence of solutions of parabolic–parabolic system to a solution of parabolic–elliptic one, when a suitable parameter in the system under consideration converges towards zero.

Keywords: nonlinear parabolic–elliptic system, nonlinear parabolic–parabolic system, chemotaxis, Keller–Segel model, pseudomeasure space

DOI: 10.3233/ASY-2008-0907

Citation: Asymptotic Analysis, vol. 61, no. 1, pp. 35-59, 2009

Price: EUR 27.50
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