Asymptotic Analysis - Volume 6, issue 2

Authors: Friedman, Avner | Hu, Bei

Article Type: Research Article

Abstract: By gradually decreasing the ambient magnetic field, under isothermal conditions, a superconductor material (of “type I”) will develop two phases separated by a thin interface Γ(t). In the “normal” conducting phase the magnetic field $\vec{H}$ is divergence free and satisfies the heat equation, whereas on the interface Γ(t), curl $\vec{H}\times n=-V_{n}\vec{H}$ where n is the normal and Vn the velocity of Γ(t); further, $|\vec{H}|=H_{c}$ (constant) on Γ(t). This free boundary problem is studied in the present paper. Existence, uniqueness and asymptotic behavior are established under assumptions which enable us to reduce the 3-dimensional …problem to a problem depending on essentially one-dimensional space variable. Show more

DOI: 10.3233/ASY-1992-6201

Citation: Asymptotic Analysis, vol. 6, no. 2, pp. 109-133, 1992

Authors: Golse, F. | Poupaud, F.

Article Type: Research Article

Abstract: On étudie la limite fluide d'un système d'équations cinétiques de la physique des semi-conducteurs pour une statistique de Fermi-Dirac. On établit que les concentrations d'électrons et de trous vérifient, quand le libre parcours moyen tend vers zéro, un système d'équations paraboliques non linéaires. La démonstration repose sur des estimations d'entropie et sur un lemme de compacité en moyenne pour l'opérateur d'advection.

DOI: 10.3233/ASY-1992-6202

Citation: Asymptotic Analysis, vol. 6, no. 2, pp. 135-160, 1992

Authors: Weck, N. | Witsch, K.J.

Article Type: Research Article

Abstract: The order of convergence for the low frequency asymptotics of general exterior problems for the Helmholtz equation with variable, possibly nonsmooth coefficients in dimensions greater than two is shown to be ω2 , the square of the frequency, except of some singular cases. In these cases the asymptotics are characterized completely by some lower order terms in the spherical harmonics expansion of the solution to the static problem.

DOI: 10.3233/ASY-1992-6203

Citation: Asymptotic Analysis, vol. 6, no. 2, pp. 161-172, 1992

Authors: Aganović, I. | Mikelić, A.

Article Type: Research Article

Abstract: The homogenization of nonstationary flow of a general two-constituant mixture in a domain with a grained boundary (porous medium) is considered. A convergence theorem for the homogenization process, together with a uniqueness theorem for a homogenized problem, is proved. The homogenized system turns out to be the widely used engineering model of miscible flow through a porous medium.

DOI: 10.3233/ASY-1992-6204

Citation: Asymptotic Analysis, vol. 6, no. 2, pp. 173-189, 1992

Authors: Chen, Goong | Huang, Falun | Lin, Chin-Yuan

Article Type: Research Article

Abstract: For the wave equation with an impedance boundary condition in a bounded domain, it is known that its energy will decay uniformly exponentially provided that the domain has, e.g., a star-shaped geometry (Chen, 1979; Lagnese, 1983). So it appears natural at first sight that the energy decay rates should increase when there is additional energy dissipation on the boundary contributed by higher-order tangential derivatives. In this paper, we study the evolution of the wave equation with such higher-order tangential dissipative boundary conditions. By using a geometrical optics expansion and a wave method argument, we show by an example on a …2-dimensional disk that at high frequencies the highest-order derivative in the boundary condition is dominant, and there is no uniform exponential decay for such modes. This constitutes a counterexample to the seemingly natural “comparison theorem” for energy decay properties. Show more

DOI: 10.3233/ASY-1992-6205

Citation: Asymptotic Analysis, vol. 6, no. 2, pp. 191-203, 1992