Asymptotic Analysis - Volume 22, issue 1

Authors: Guesmia, Aissa

Article Type: Research Article

Abstract: We prove some precise decay estimates of the energy for non‐isotropic elastodynamic systems with some localized dissipations. The damping is nonlinear and is effective only in a neighborhood of a suitable subset of the boundary, we study both degenerate and nondegenerate cases. The method of proof is direct and is based on the multiplier technique and on some specific integral inequalities.

Keywords: Decay, localized dissipation, elasticity system, multiplier method

Citation: Asymptotic Analysis, vol. 22, no. 1, pp. 1-13, 2000

Authors: Bresch, Didier | Lemoine, Jérôme | Simon, Jacques

Article Type: Research Article

Abstract: In this paper we study the behaviour of solutions of Navier–Stokes equations with adherence to the bottom and traction by wind at the surface when the aspect ratio \delta=\hbox{depth}/\hbox{lenght} of the domain tends to 0. Precisely, we prove that when wind is moderate, a variational solution converges to the solution of a vertical diffusion model. This model is either quasistationary or nonstationary, according to the characteristic time.

Keywords: Navier–Stokes equations, wind driven, Coriolis force, asymptotic model, shallow water

Citation: Asymptotic Analysis, vol. 22, no. 1, pp. 15-38, 2000

Authors: Morame, Abderemane | Truc, Françoise

Article Type: Research Article

Abstract: We give the asymptotic behaviour, when h tends to zero, of the number of eigenvalues less then a fixed energy \lambda , of the Schrödinger operator {\widehat{H}_h}=-h^2\Delta + f(x)g(y),\ (x,y)\in \mathbf{R}^d=\mathbf{R}^n\times \mathbf{R}^m . f and g are continuous and positive functions tending to infinity at infinity, g(y) is homogeneous and f(x)>0 .

Citation: Asymptotic Analysis, vol. 22, no. 1, pp. 39-49, 2000

Authors: Ortega, Jaime H. | Zuazua, Enrique

Article Type: Research Article

Abstract: In this paper we study the asymptotic behavior of solutions of linear parabolic equations in \mathbb{R}^N with periodic coefficients and L^1 initial data, as t\rightarrow \infty . It was already known that, in a first approximation, solutions behave as the fundamental solution of the homogenized system. We use the Bloch waves decomposition to obtain a complete expansion of the solutions as t\rightarrow \infty .

Citation: Asymptotic Analysis, vol. 22, no. 1, pp. 51-85, 2000