Asymptotic Analysis - Volume 30, issue 3-4

Authors: Bayada, G. | Chambat, M. | Gamouana, S.R.

Article Type: Research Article

Abstract: We study the coupling of a porous medium and an adjacent thin film flow, taking account of non‐Newtonian effects induced by additives in the fluid. The starting point is the micropolar Stokes system. A critical relation between η, the thin gap height size and ε, the characteristic size of the pores in the porous medium is exhibited. Asymptotic equations are obtained including the continuity of the pressure at the interface. The influence of the rheological micropolar parameters is discussed and various asymptotic behaviours are identified: the micropolar effects are found to be significant in both media, or only in the …porous medium, or can be neglected everywhere. Show more

Citation: Asymptotic Analysis, vol. 30, no. 3-4, pp. 187-216, 2002

Authors: Cardoso, Fernando | Popov, Georgi

Article Type: Research Article

Abstract: The aim of this paper is to construct compactly supported Gevrey quasimodes with exponentially small discrepancy for the Laplace operator with Dirichlet boundary conditions in a domain X with analytic boundary. The quasimodes are associated with a nondegenerate elliptic closed broken geodesic γ in X. We find a Cantor family Λ of invariant tori of the corresponding Poincaré map which is Gevrey smooth with respect to the transversal variables (the frequencies). Quantizing the Gevrey family Λ, we construct quasimodes with exponentially small discrepancy. As a consequence, we obtain a large amount of resonances exponentially close to the real axis for …suitable compact obstacles. Show more

Citation: Asymptotic Analysis, vol. 30, no. 3-4, pp. 217-247, 2002

Authors: Byeon, Jaeyoung

Article Type: Research Article

Abstract: We consider the problem: Δu+up =0 in ΩR ,u=0 on ∂ΩR ,u>0 in ΩR , where ΩR ≡{x∈RN |R−1<|x|<R+1}, N≥3, and 1<p<(N+2)/(N−2). This problem is invariant under the orthogonal coordinate transformations, in other words, O(N)‐symmetric. Let G be a closed subgroup O(N), and HG R ≡{u∈H0 1,2 (RN ) |u(x)=u(gx), x∈ΩR , g∈G}. In the earlier paper [5], an existence of locally minimal energy solutions in HG R due to a structural property of the orbits space of an action G×SN−1 →SN−1 was showed for large R. In this paper, it will be showed that more various types of solutions …than those obtained in [5], which are close to a finite sum of locally minimal energy solutions in HR G for some G⊂O(N), appear as R→∞. Furthermore, we discuss possible types of solutions and show that any solution with exactly two local maximum points should be O(N−1)‐symmetric for large R>0. Show more

Keywords: nonlinear elliptic, symmetry, group actions, orbits

Citation: Asymptotic Analysis, vol. 30, no. 3-4, pp. 249-272, 2002

Authors: Mokhtar‐Kharroubi, M. | Thevenot, L.

Article Type: Research Article

Abstract: We give a spectral approach to the diffusion approximation for general neutron transport equations on the torus with a particular emphasis on the initial layer problem. By Fourier analysis, we diagonalize the transport operator and deal with diffusive limit for each Fourier mode by a Dunford functional calculus.

Keywords: transport equation, diffusion limit, initial layer, spectral theory, Dunford calculus, even parity formalism

Citation: Asymptotic Analysis, vol. 30, no. 3-4, pp. 273-300, 2002

Authors: Aassila, Mohammed

Article Type: Research Article

Abstract: In this paper we study the global existence and nonexistence problems for the Klein–Gordon equation with nonlinear damping and nonlinear perturbation.

Citation: Asymptotic Analysis, vol. 30, no. 3-4, pp. 301-311, 2002

Authors: Conrad, Francis | O'Dowd, Geoffrey | Saouri, Fatima‐Zahra

Article Type: Research Article

Abstract: We consider a model of an overhead crane where the boundary feedback takes into account the velocity, but not the position. In this noncoercive case, we prove that asymptotically the system converges to a rest position which depends on the initial data. The case of linear and (more sophisticated) nonlinear feedbacks is presented.

Keywords: flexible structure, boundary control, asymptotic behaviour

Citation: Asymptotic Analysis, vol. 30, no. 3-4, pp. 313-330, 2002

Authors: Ammari, Habib | Volkov, Darko

Article Type: Research Article

Abstract: We consider electromagnetic media that consist of a homogeneous (constant coefficient) electromagnetic material with a finite number of small dielectric imperfections. For such media, we provide a rigorous derivation of asymptotic formulas for perturbations in the eigenfrequencies of the full Maxwell equations caused by the presence of the dielectric imperfections.

Keywords: Maxwell's equations, eigenvalues, asymptotics, small dielectric imperfections

Citation: Asymptotic Analysis, vol. 30, no. 3-4, pp. 331-350, 2002

Article Type: Other

Citation: Asymptotic Analysis, vol. 30, no. 3-4, pp. 351-352, 2002

Article Type: Other

Citation: Asymptotic Analysis, vol. 30, no. 3-4, pp. 353-360, 2002