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The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand.
Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
Authors: Chacha, D. | Sanchez-Palencia, E.
Article Type: Research Article
Abstract: We consider the macroscopic behavior of an elastic plate containing many small fissures distributed periodically, the period being of the same order as the thickness of the plate. In the fissures a one-side constraint of the Signorini's kind is prescribed. The macroscopic behavior involves a nonlinear monotone strain-stress law, and coupling of tensions and flexions.
DOI: 10.3233/ASY-1992-5501
Citation: Asymptotic Analysis, vol. 5, no. 5, pp. 381-396, 1992
Authors: De Arcangelis, Riccardo | Vitolo, Antonio
Article Type: Research Article
Abstract: For every bounded open set Ω with Lipschitz boundary, β in L∞ (Ω) we study the asymptotic behaviour (as h→∞) of the sequence ih (Ω,β)=inf {∫Ω f(hx,Du)+∫Ω βu, u Lipschitz continuous, u=0 on ∂Ω,|Du(x)|≤ϕ(hx) for a.e. x in Ω} where f is a nonnegative function on Rn ×Rn measurable and ]0,1[n -periodic in the x variable, convex in the z variable, ϕ is a ]0,1[n -periodic function from Rn into [0,+∞] such that there exist Θ∈[0,½[, m>0 with 0<m≤ϕ(x) for a.e. x in ]0,1[n −]½−Θ, ½+Θ[n , and one of the following conditions hold: f|z|p ≤f(x,z), p>n; or ϕ∈Lp …(]0,1[n ) p>n. It is proved that ih (Ω,β) converges to a minimim problem of integral type for which an explicit formula is proved. Show more
DOI: 10.3233/ASY-1992-5502
Citation: Asymptotic Analysis, vol. 5, no. 5, pp. 397-428, 1992
Authors: Päivärinta, Lassi | Rempel, Stephan
Article Type: Research Article
Abstract: Let Ω be a compact submanifold of a two dimensional Riemannian manifold X having a boundary ∂Ω which is piecewise smooth without sharp peaks. We study the pseudo-differential equations Op(|ξ|±1 )u=f in Ω in appropriate function spaces. Existence and uniqueness of solutions are proven. Moreover, it is shown that they possess an asymptotic expansion near each angular point provided the right hand side does. By a Mellin operator calculus we get information about the exponent of the asymptotics. A numerical algorithm is given which yields the leading singularity. Applications to the screen problem in electrodynamics, to the charge density problem …in electrostatics and to the crack problem in elasticity are given. Show more
DOI: 10.3233/ASY-1992-5503
Citation: Asymptotic Analysis, vol. 5, no. 5, pp. 429-460, 1992
Authors: Jinhai, Yan
Article Type: Research Article
Abstract: In studying the limit behavior of the operator defined by the method HUM for the exact controllability of hyperbolic systems on a thin domain Ω×(0,ε) in Rn+1 , we observe that as ε goes to zero, this operator will not tend to the corresponding operator defined by HUM on the domain Ω in Rn . We make a correction for the operator on the thin domain so as to get the desired limit behavior.
DOI: 10.3233/ASY-1992-5504
Citation: Asymptotic Analysis, vol. 5, no. 5, pp. 461-471, 1992
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