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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.
Authors: Pauly, Dirk
Article Type: Research Article
Abstract: We continue the study of the operator of generalized Maxwell equations and completely discover the behavior of the solutions of the time-harmonic equations as the frequency tends to zero. Thereby we identify degenerate operators in terms of special ‘polynomially growing’ solutions of a corresponding static problem, which must be added to the ‘usual’ Neumann series in order to describe the low frequency asymptotic adequately.
Keywords: low frequency asymptotics, exterior boundary value problems, Maxwell's equations, variable coefficients, electro-magneto static, Hodge–Helmholtz decompositions, radiating solutions, asymptotic expansions, spherical harmonics, Hankel functions
DOI: 10.3233/ASY-2008-0898
Citation: Asymptotic Analysis, vol. 60, no. 3-4, pp. 125-184, 2008
Authors: Afendikov, Andrei | Fiedler, Bernold | Liebscher, Stefan
Article Type: Research Article
Abstract: We consider the Kolmogorov problem of viscous incompressible planar fluid flow under external spatially periodic forcing. Looking for time-independent bounded solutions near the critical Reynolds number, we use the Kirchgässner reduction to obtain a spatial dynamical system on a 6-dimensional center manifold. The dynamics is generated by translations in the unbounded spatial direction. Reduction by first integrals yields a 3-dimensional reversible system with a line of equilibria. This line of equilibria is neither induced by symmetries, nor by first integrals. At isolated points, normal hyperbolicity of the line fails due to a transverse double eigenvalue zero. In particular we describe …the complete set ℬ of all small bounded solutions. In the classical Kolmogorov case, ℬ consists of periodic profiles, homoclinic pulses and a heteroclinic front–back pair. This is a consequence of the symmetry of the external force. Show more
DOI: 10.3233/ASY-2008-0901
Citation: Asymptotic Analysis, vol. 60, no. 3-4, pp. 185-211, 2008
Authors: Takahashi, Futoshi
Article Type: Research Article
Abstract: We study the asymptotic behavior of least energy solutions to the equation Δ2 u=c0 K(x)upε with the Navier boundary condition as ε→+0, where Ω is a smooth bounded domain in RN (N≥5), c0 =(N−4)(N−2)N(N+2) and pε =(N+4)/(N−4)−ε, ε>0. Under some assumptions on the coefficient function K, we obtain fairly precise asymptotics of the L∞ -norm of least energy solutions.
Keywords: biharmonic equation, critical exponent
DOI: 10.3233/ASY-2008-0904
Citation: Asymptotic Analysis, vol. 60, no. 3-4, pp. 213-226, 2008
Authors: Andreucci, Daniele | Tedeev, Anatoli F.
Article Type: Research Article
Abstract: We consider the Cauchy problem for a doubly nonlinear parabolic equation, obtaining optimal estimates both for the sup norm of nonnegative solutions, and for their support for large times.
Keywords: convection–diffusion equation, long-time behaviour, finite speed of propagation, entropy inequality
DOI: 10.3233/ASY-2008-0906
Citation: Asymptotic Analysis, vol. 60, no. 3-4, pp. 227-247, 2008
Article Type: Other
Citation: Asymptotic Analysis, vol. 60, no. 3-4, pp. 249-249, 2008
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