Asymptotic Analysis - Volume 8, issue 3

Authors: Eidus, D.

Article Type: Research Article

Abstract: The large time asymptotics of solutions of the Cauchy problem for a non-homogeneous wave equation with a periodic perturbation is found under some restrictions, imposed on the corresponding operator. We apply the obtained results to the third boundary value problem for the wave equation in a half-space.

DOI: 10.3233/ASY-1994-8301

Citation: Asymptotic Analysis, vol. 8, no. 3, pp. 217-236, 1994

Authors: Galaktionov, Victor A. | Kersner, Róbert | Vazquez, Juan L.

Article Type: Research Article

Abstract: We study the large-time behaviour of the solution to the mixed problem: ut =Δ(e−1/u ) in Q=Ω×(0,∞), with u(x, t) = 0 for x∈∂Ω, t≥0 and u(x,0)∈L∞ (Ω), u(x,0)≥0. Ω is a bounded domain with smooth boundary ∂Ω. We show that there exists a function F(x) > 0 in Ω such that as t→∞ t(log t)2 e−1/u →F(x) uniformly in x∈Ω. The function F is uniquely determined as the solution of the problem: ΔF=−1 in Ω, F=0 on ∂Ω.

DOI: 10.3233/ASY-1994-8302

Citation: Asymptotic Analysis, vol. 8, no. 3, pp. 237-246, 1994

Authors: Alberti, Giovanni | Ambrosio, Luigi | Buttazzo, Giuseppe

Article Type: Research Article

Abstract: In this paper we study the asymptotic behaviour of the functionals Fε (u)=∫Ω [ε|∇u|2 +ε−3 β(u/ε)]dx where β is a non-negative lower semicontinuous function with compact support. When ε tends to 0, the limit functional corresponds to a least area problem with an obstacle.

DOI: 10.3233/ASY-1994-8303

Citation: Asymptotic Analysis, vol. 8, no. 3, pp. 247-258, 1994

Authors: Rao, Bopeng

Article Type: Research Article

Abstract: We consider a non-linear model of elastic spherical shell subjected to suitable hydrostatic pressure. Applying the method of asymptotic expansions to the general three-dimensional equilibrium equations, it is shown that the leading term of the expansions is a solution of a known two-dimensional model in non-linear shell theory.

DOI: 10.3233/ASY-1994-8304

Citation: Asymptotic Analysis, vol. 8, no. 3, pp. 259-276, 1994

Authors: Bethuel, Fabrice | Ghidaglia, Jean-Michel

Article Type: Research Article

Abstract: In this work we show that any sequence uε of smooth solutions to the steady incompressible two-dimensional Euler equation in a bounded domain Ω, which converges weakly in L2 (Ω) as ε goes to zero, converges to a weak solution of this equation provided curl uε remains bounded in L1 (Ω).

DOI: 10.3233/ASY-1994-8305

Citation: Asymptotic Analysis, vol. 8, no. 3, pp. 277-291, 1994

Authors: Roch, Steffen | Silbermann, Bernd

Article Type: Research Article

Abstract: The paper is devoted to the asymptotic behavior of the eigenvalues and singular values of Toeplitz and Hankel matrices with piecewise continuous generating functions. The central result is a norm stability theorem for sequences of matrices belonging to a Banach algebra of Toeplitz operators. This theorem applies to derive a complete description of the partial and the uniform limiting set of the eigenvalues and the singular values of the matrices under consideration.

DOI: 10.3233/ASY-1994-8306

Citation: Asymptotic Analysis, vol. 8, no. 3, pp. 293-309, 1994