Asymptotic Analysis - Volume 25, issue 2

Authors: Buet, C. | Cordier, S. | Lucquin‐Desreux, B.

Article Type: Research Article

Abstract: The Lorentz operators are derived from either Boltzmann or Fokker–Planck collisions operators when considering a mixture of species with disparate masses [8]. The Fokker–Planck operator is the so called “grazing collision limit” of the Boltzmann operator as proved in [1,12,7]. In our simpler case, we improve the results by proving uniform in time convergence and by controling the speed of the trend to equilibrium. The results are based on a spectral analysis of the operators which share the same basis of eigenfunctions.

Citation: Asymptotic Analysis, vol. 25, no. 2, pp. 93-107, 2001

Authors: Reyes, G.

Article Type: Research Article

Abstract: In this paper we study the intermediate asymptotics as t→∞ of nontrivial, nonnegative solutions to the Cauchy problem for the following nonlinear first order equation: ut +(um )x +up =0, with m>1, p=m+1. We prove that for any bounded, nonnegative, compactly supported initial data the asymptotic behaviour is given in first approximation by a universal function W, which is a contracted “N‐wave” with logarithmically decaying mass.

Citation: Asymptotic Analysis, vol. 25, no. 2, pp. 109-122, 2001

Authors: Immink, G.K.

Article Type: Research Article

Abstract: We define a “weak Borel‐sum” for a class of formal power series. This is a generalization of the ordinary Borel‐sum with applications in the theory of locally analytic difference equations. We explain its relation to a particular type of accelero‐sum obtained by the use of a weak acceleration operator, and briefly discuss a corresponding Stokes phenomenon. Most results of this paper are based on the quasi‐analyticity of a certain type of Borel transform.

Citation: Asymptotic Analysis, vol. 25, no. 2, pp. 123-148, 2001

Authors: Malchiodi, Andrea

Article Type: Research Article

Abstract: We deal with a Newtonian system like $\ddot{x}$ +V′(x)=0. We suppose that V :${\mathbb{R}}$ n →${\mathbb{R}}$ possesses an (n−1)‐dimensional compact manifold M of critical points, and we prove the existence of arbitrarily slow periodic orbits. When the period tends to infinity these orbits, rescaled in time, converge to some closed geodesics on M.

Keywords: Closed geodesics, slow motion, periodic solutions, limit trajectories

Citation: Asymptotic Analysis, vol. 25, no. 2, pp. 149-181, 2001