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Asymptotic Analysis - Volume 93, issue 3

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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.

The nonlinear 2D supercritical inviscid shallow water equations in a rectangle

Authors: Huang, Aimin | Petcu, Madalina | Temam, Roger

Article Type: Research Article

Abstract: In this article we consider the inviscid two-dimensional shallow water equations in a rectangle. The flow occurs near a stationary solution in the so called supercritical regime and we establish short term existence of smooth solutions for the corresponding initial and boundary value problem.

Keywords: shallow water equations, inviscid flow, initial and boundary value problems

DOI: 10.3233/ASY-151293

Citation: Asymptotic Analysis, vol. 93, no. 3, pp. 187-218, 2015

Price: EUR 27.50

Mathematical justification of macroscopic models for diffusion MRI through the periodic unfolding method

Authors: Coatléven, Julien

Article Type: Research Article

Abstract: Diffusion Magnetic Resonance Imaging (dMRI) is a promising tool to obtain useful information on cellular structure when applied to biological tissues. A coupled macroscopic model has been introduced recently through formal homogenization to model dMRI’s signal attenuation. This model was based on a particular scaling of the permeability condition modeling cellular membranes. In this article, we explore all the possible scalings and mathematically justify the corresponding limit models, using the periodic unfolding method. We also illustrate through numerical simulations the respective behavior of the limit models when compared to dMRI measurements.

Keywords: diffusion MRI, homogenization, Bloch–Torrey equation, periodic unfolding, imperfect transmission, trace jumps

DOI: 10.3233/ASY-151294

Citation: Asymptotic Analysis, vol. 93, no. 3, pp. 219-258, 2015

Price: EUR 27.50

Combined effects of concave–convex nonlinearities and indefinite potential in some elliptic problems

Authors: Papageorgiou, Nikolaos S. | Rădulescu, Vicenţiu D.

Article Type: Research Article

Abstract: We consider a nonlinear Dirichlet problem driven by the p -Laplacian and a reaction which exhibits the combined effects of concave (that is, sublinear) terms and of convex (that is, superlinear) terms. The concave term is indefinite and the convex term need not satisfy the usual in such cases Ambrosetti–Rabinowitz condition. We prove a bifurcation-type result describing the set of positive solutions as the positive parameter λ varies.

Keywords: indefinite concave term, superlinear perturbation, p-Laplacian, nonlinear regularity, positive solutions

DOI: 10.3233/ASY-151292

Citation: Asymptotic Analysis, vol. 93, no. 3, pp. 259-279, 2015

Price: EUR 27.50
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