Asymptotic Analysis - Volume 29, issue 2

Authors: Bruneau, Vincent | Carbou, Gilles

Article Type: Research Article

Abstract: In this paper, we study a singular perturbation of an eigenvalues problem related to supra‐conductor wave guides. Using boundary layer tools we perform a complete asymptotic expansion of the eigenvalues as the conductivity tends to +∞.

Citation: Asymptotic Analysis, vol. 29, no. 2, pp. 91-113, 2002

Authors: Sanz, Javier

Article Type: Research Article

Abstract: In this paper a theory of summability in a direction, extending that of J.P. Ramis, is developed for formal power series of several variables. To this end, generalized Laplace and Borel transforms are studied, as well as their action on functions admitting Gevrey strongly asymptotic expansion as defined by H. Majima. The definition we give of summability in a direction turns out to be, in a sense, equivalent to an iterative classical summation procedure. As an application we provide a new proof of a well‐known result of R. Gérard and Y. Sibuya stating the convergence of the formal power series …solution to a certain completely integrable Pfaffian system. Show more

Citation: Asymptotic Analysis, vol. 29, no. 2, pp. 115-141, 2002

Authors: Andreu, F. | Mazón, J.M. | Simondon, F. | Toledo, J.

Article Type: Research Article

Abstract: For nonlinear parabolic equations of the form ut =Δum −uμ ‖∇um ‖q +up , we prove nonexistence of global admissible solutions for large initial data for some range of the parameters m, μ, q and p. To do so we use comparison with suitable blowing up self‐similar subsolutions. We also prove that for the complementary range of the parameters for which we obtain blow‐up, there exists globally bounded admissible solutions.

Keywords: nonlinear parabolic equations, admissible solution, finite time blow‐up, gradient term

Citation: Asymptotic Analysis, vol. 29, no. 2, pp. 143-155, 2002

Authors: Bardos, Claude | Fink, Mathias

Article Type: Research Article

Abstract: In the present paper a mathematical analysis of the “time reversal mirror” (cf. [4,9,10]) is given. As a first step of a more detailed program, the emphasis is put on phenomena which are described by the genuine acoustic equation with Dirichlet or “impedance” boundary conditions. An ideal situation is first considered then relation between the question of the local decay of energy and the accuracy of the method are exploited. The positive effect of the ergodicity is explained and eventually comparison with control theory approach is considered.

Citation: Asymptotic Analysis, vol. 29, no. 2, pp. 157-182, 2002

Article Type: Correction

Citation: Asymptotic Analysis, vol. 29, no. 2, pp. 183-183, 2002