Asymptotic Analysis - Volume 6, issue 4

Authors: Märker, Fritz Jürgen

Article Type: Research Article

Abstract: Riccati matrix differential equations of a specific form correspond to self-adjoint differential equations of Sturm–Liouville type (containing an eigenvalue parameter). We derive the asymptotic behaviour of solutions of such a Riccati equation as the parameter tends to minus infinity. Such results can be used e.g. to handle certain problems in optimal control theory.

DOI: 10.3233/ASY-1993-6401

Citation: Asymptotic Analysis, vol. 6, no. 4, pp. 295-314, 1993

Authors: Desvillettes, Laurent

Article Type: Research Article

Abstract: We study the convergence of splitting algorithms for the radiative transfer equation and for the Vlasov–Maxwell system of equations.

DOI: 10.3233/ASY-1993-6402

Citation: Asymptotic Analysis, vol. 6, no. 4, pp. 315-333, 1993

Authors: Gingold, H.

Article Type: Research Article

Abstract: Given a second-order linear differential equation y″=ϕ(x,ε)y. Let ϕ(x,ε) be a meromorphic real-valued function of two independent variables x and ε. x is allowed to vary on an interval [a,b] and ε varies on (0,ε0 ]. The approximation of its solutions, as well as of their derivatives as ε→0+ are provided for the entire interval [a,b] in the presence of several-coalescing transition points. Approximations on closed subintervals of [a,b] are provided. The end points of those subintervals are allowed to coincide with turning points. The approximations given could replace a nonrigorous analysis in the literature which had similar …goals and in which an error was found. The formulas could prove to be useful for numerical implementation in problems of wave propagation in inhomogeneous medium. Our methods avoid analytic continuation, Langer transformations and special functions. Show more

DOI: 10.3233/ASY-1993-6403

Citation: Asymptotic Analysis, vol. 6, no. 4, pp. 335-364, 1993

Authors: Conca, C. | Planchard, J. | Vanninathan, M.

Article Type: Research Article

Abstract: The aim of this paper is the asymptotic analysis of a spectral problem which involves Helmholtz' equation coupled with a nonlocal Neumann boundary condition on the boundary of a periodic perforated domain of R2 . This eigenvalue problem represents the vibrations (eigenfrequencies and eigenmotions) of a tube-bundle immersed in a perfect compressible fluid. Our analysis of convergence shows that the vibrations of this fluid–solid structure with a large number of tubes are close to the spectrum of an unbounded operator in a Hilbert space. Using the method of Bloch and exploiting the periodic structure of the problem, we derive the …spectral family of this limit operator and we prove that its spectrum can be completely determined by only computing local eigenvalue problems in the basic cell representing the periodic structure in the problem. Show more

DOI: 10.3233/ASY-1993-6404

Citation: Asymptotic Analysis, vol. 6, no. 4, pp. 365-389, 1993

Article Type: Other

Citation: Asymptotic Analysis, vol. 6, no. 4, pp. 391-391, 1993