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Asymptotic Analysis - Volume 78, issue 4

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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 behaviour near a nonlinear sink

Authors: Calder, Matt S. | Siegel, David

Article Type: Research Article

Abstract: In this paper, we will develop an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Moreover, we will address the writing of one component of a solution in terms of the other in the case of a planar system. Examples will be given, notably the Michaelis–Menten mechanism of enzyme kinetics.

Keywords: asymptotics, differential equations, iteration, resonance, sink, concavity, enzyme, Michaelis–Menten

DOI: 10.3233/ASY-2011-1082

Citation: Asymptotic Analysis, vol. 78, no. 4, pp. 187-215, 2012

Price: EUR 27.50

Long-time behavior for the Hele–Shaw–Cahn–Hilliard system

Authors: Wang, Xiaoming | Wu, Hao

Article Type: Research Article

Abstract: We study the Hele–Shaw–Cahn–Hilliard system that models two phase incompressible Darcian flow in porous media with matched density but arbitrary viscosity contrast. In the 3D case, we prove eventual regularity of weak solutions, as well as existence of global classical solutions if either the Péclet number is sufficiently small or the initial datum is close to one local energy minimizer of the free energy. In both 2D and 3D, we demonstrate that the ω-limit set of each trajectory consists of a single steady state. Finally, stability of local minimizers is established.

Keywords: Hele–Shaw–Cahn–Hilliard system, eventual regularity, convergence to equilibrium, stability

DOI: 10.3233/ASY-2012-1092

Citation: Asymptotic Analysis, vol. 78, no. 4, pp. 217-245, 2012

Price: EUR 27.50

Author Index Volume 78 (2012)

Article Type: Other

Citation: Asymptotic Analysis, vol. 78, no. 4, pp. 247-247, 2012

Price: EUR 27.50
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