Asymptotic Analysis - Volume 11, issue 1

Authors: Guillopé, Laurent | Zworski, Maciej

Article Type: Research Article

Abstract: Let X be a conformally compact n-dimensional manifold with constant negative curvature −1 near infinity. The resolvent (Δ−s(n−1−s))−1 , Res>n−1, of the Laplacian on X extends to a meromorphic family of operators on C and its poles are called resonances or scattering poles. If NX (r) is the number of resonances in a disc of radius r we prove the following upper bound: NX (r)≤Crn+1 +C.

DOI: 10.3233/ASY-1995-11101

Citation: Asymptotic Analysis, vol. 11, no. 1, pp. 1-22, 1995

Authors: Haario, Heikki | Rivkind, Valeri

Article Type: Research Article

Abstract: We consider a reaction-diffusion system with fast reaction. An asymptotic analysis is performed, and an analytical expression for the thickness the essential reaction zone is derived.

DOI: 10.3233/ASY-1995-11102

Citation: Asymptotic Analysis, vol. 11, no. 1, pp. 23-30, 1995

Authors: Xin, J. | Peirce, A. | Chadam, J. | Ortoleva, P.

Article Type: Research Article

Abstract: A model of reactive flow in a layered porous medium is considered in which the layering is represented by small-scale periodic structure. A novel form of homogenization analysis is presented, combining geometric optics and multiple scales expansions together with matched asymptotics to derive an effective free boundary problem for the motion of the reactive interface. Applications of the effective free boundary equations are given in which travelling wave solutions and the stability of shape perturbations are considered.

DOI: 10.3233/ASY-1995-11103

Citation: Asymptotic Analysis, vol. 11, no. 1, pp. 31-54, 1995

Authors: Naumann, J.

Article Type: Research Article

Abstract: The paper is concerned with the non-stationary semiconductor equations (van Roosbroeck's system) involving a gradient non-linearity which models the generation of particles due to impact ionization. We establish the existence of a weak solution to this system over a cylinder Ω×(0,T1 ) (Ω⊂R2 bounded domain, (0, T1 ) small time interval). The method of proof relies on approximating the generation term by bounded gradient non-linearities.

DOI: 10.3233/ASY-1995-11104

Citation: Asymptotic Analysis, vol. 11, no. 1, pp. 55-72, 1995

Authors: Veiga, M.F.

Article Type: Research Article

Abstract: In the framework of linearized elasticity, the asymptotic expansion method is used to obtain an approximation of the displacement field of a beam with a variable cross section (in the sense that the section rotates along the longitudinal axis of the beam, keeping its form). We give a complete characterization of the equations governing the bending, stretching and torsion components, generalizing, in this way, previous results for straight beams.

DOI: 10.3233/ASY-1995-11105

Citation: Asymptotic Analysis, vol. 11, no. 1, pp. 73-105, 1995