Asymptotic Analysis - Volume 60, issue 3-4

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