Asymptotic Analysis - Volume 24, issue 2

Authors: Liu, Wei‐Jiu

Article Type: Research Article

Abstract: In this paper we test the robustness of a nonlinear boundary feedback control for a flexible beam with respect to perturbation. We show that additional dynamics of perturbation at one of the ends of the beam, as long as they are strictly passive, will not destabilize the controlled beam.

Keywords: Flexible beam, robustness, stability, Lyapunov method

Citation: Asymptotic Analysis, vol. 24, no. 2, pp. 91-105, 2000

Authors: Fermanian Kammerer, C.

Article Type: Research Article

Abstract: In this paper we study families of solutions to heat equation with a small parameter and a propagation term consisting in a discontinuous vector field b through a smooth compact hypersurface S. Our purpose is to describe the evolution of the energy density as h goes to 0 of a family of solutions for a bounded square integrable family of inital data. Outside of S it is classical to calculate this limit by using semi‐classical measures associated with the family of solutions. The discontinuity of b through S induces a difficulty that we overcome provided a second microlocalization. We introduce …two‐microlocal items describing the concentration of a square integrable bounded sequence on a hypersurface. By using these items we calculate for convenient times semi‐classical measures of the family of solutions in the whole cotangent space and the limit of the energy density as small parameter goes to 0. Show more

Citation: Asymptotic Analysis, vol. 24, no. 2, pp. 107-141, 2000

Authors: Capdeboscq, Yves

Article Type: Research Article

Abstract: In this paper is studied the homogenization of an evolution problem for a cooperative system of weakly coupled elliptic partial differential equations, called neutronic multigroup diffusion model, in a periodic heterogenous domain. Such a model is used for studying the evolution of the neutron flux in nuclear reactor core. In this paper, we show that under a symmetry assumption, the oscillatory behavior of the solutions is controled by the first eigenvector of a multigroup eigenvalue problem posed in the periodicity cell, whereas the global trend is asymptotically given by a homogenized evolution problem. We then turn to cases when the …symmetry condition is not fulfilled. In domains without boundaries, the limit equation for the global trend is then a homogenized transport equation. Alternatively, we show that in bounded domains and with well prepared initial data, the microscopic scale does not only control the oscillatory behavior of the solutions, but also induces an exponential drift. Show more

Citation: Asymptotic Analysis, vol. 24, no. 2, pp. 143-165, 2000

Authors: Hernández, Jesús A. | Sanz, Javier

Article Type: Research Article

Abstract: We give constructive proofs for two Borel–Ritt interpolation results, stating the existence of holomorphic functions on polysectors admitting an arbitrarily prescribed asymptotic expansion, whether in the sense of Gérard–Sibuya or in that of Majima. As a consequence, a new proof is obtained for the classical Borel's theorem on the existence of 𝒞∞ functions on $\mathbb{R}^{n}$ with given derivatives at 0; in fact, our construction provides functions analytic in $(\mathbb{R}-\{0\})^{n}$ .

Citation: Asymptotic Analysis, vol. 24, no. 2, pp. 167-182, 2000