Asymptotic Analysis - Volume 54, issue 1-2

Authors: Agarwal, Ravi P. | Djebali, Smail | Moussaoui, Toufik | Mustafa, Octavian G. | Rogovchenko, Yuri V.

Article Type: Research Article

Abstract: We discuss a number of issues important for the asymptotic integration of ordinary differential equations. After developing the tools required for application of the fixed point theory in the investigation, we present some general results about the long-time behavior of solutions of n-th order nonlinear differential equations with an emphasis on the existence of polynomial-like solutions, the asymptotic representation for the derivatives and the effect of perturbations upon the asymptotic behavior of solutions.

Citation: Asymptotic Analysis, vol. 54, no. 1-2, pp. 1-50, 2007

Authors: Li, Fushan

Article Type: Research Article

Abstract: By asymptotic analysis, we prove that the displacement of linearly viscoelastic Koiter's shell equations converges to the solution of two-dimensional linearly viscoelastic membrane shell or flexural shell model problem.

Keywords: asymptotic analysis, membrane shells, flexural shells, Koiter's shells

Citation: Asymptotic Analysis, vol. 54, no. 1-2, pp. 51-70, 2007

Authors: Wu, Hao

Article Type: Research Article

Abstract: In this paper we consider a Cahn–Hilliard model endowed with the Wentzell boundary condition, which arises from the study of spinodal decomposition in binary mixtures confined to a bounded domain with permeable wall. Under the assumption that the nonlinearity is analytic with respect to the unknown dependent function, we prove the convergence of a global solution to an equilibrium as time goes to infinity by means of an extended Łojasiewicz–Simon type inequality with boundary term. Estimates of the convergence rate are also obtained.

Keywords: Cahn–Hilliard equation, Wentzell boundary condition, Łojasiewicz–Simon inequality, convergence to equilibrium

Citation: Asymptotic Analysis, vol. 54, no. 1-2, pp. 71-92, 2007

Authors: Hu, Weiwei | Shen, Zifei | Xin, Yuhong | Zhu, Guangtian

Article Type: Research Article

Abstract: This paper is devoted to investigating the exponential stability of a kind of repairable system with cold standby units, imperfect switching mechanism and multiple non-critical and critical errors. We have known that the system operator generates a positive C0 -semigroup of contractions and will show its quasi-compactness and irreducibility. Further, 0 is a simple eigenvalue of the system operator. As a result, we obtain that the time-dependent solution of the system converges to the steady-state solution exponentially, which is the positive eigenfunction corresponding to the simple eigenvalue 0.

Keywords: C_0-semigroup, quasi-compact, essential growth bound, exponential stability

Citation: Asymptotic Analysis, vol. 54, no. 1-2, pp. 93-102, 2007

Authors: Onofrei, D. | Vernescu, B.

Article Type: Research Article

Abstract: In this paper we present new results regarding the H1 0 -norm error estimate for the classical problem in homogenization using suitable boundary layer correctors. Compared with all the existing results on the subject, which assume either smooth enough coefficients or smooth data, we use the periodic unfolding method and propose a new asymptotic series to approximate the solution uε with an error estimate which holds true for nonsmooth coefficients and general data.

Citation: Asymptotic Analysis, vol. 54, no. 1-2, pp. 103-123, 2007