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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: Eidus, D.
Article Type: Research Article
DOI: 10.3233/ASY-1989-2201
Citation: Asymptotic Analysis, vol. 2, no. 2, pp. 95-99, 1989
Authors: Sweers, G.
Article Type: Research Article
Abstract: In this paper we study two-sided a-priori estimates in Lp -type spaces for a class of singularly perturbed elliptic problems with Dirichlet boundary conditions.
DOI: 10.3233/ASY-1989-2202
Citation: Asymptotic Analysis, vol. 2, no. 2, pp. 101-138, 1989
Authors: Schäfke, Reinhard | Volkmer, Hans
Article Type: Research Article
Abstract: We derive bounds for the values of L2 -normalized eigenfunctions of Sturm–Liouville systems containing k spectral parameters λ1 ,…,λk . In the case of continuous coefficients this bound is of order O(|λ|k/4 as |λ|→∞, where λ=(λ1 ,…,λk ) is the corresponding eigenvalue and |λ|=max|λi |. If the coefficients are continuously differentiable then we obtain a better bound of order O(|λ|(k−1)/6 ). The latter result generalizes a bound of order O(|λ|1/6 ) given by Faierman (1980) in the two-parameter case k = 2 under the assumption of analytic coefficients. We show by examples that the powers ¼k and ⅙(k−1) of …|λ| in the above bounds are optimal. Show more
DOI: 10.3233/ASY-1989-2203
Citation: Asymptotic Analysis, vol. 2, no. 2, pp. 139-159, 1989
Authors: Bertrand, Pierre
Article Type: Research Article
Abstract: We give the development of jε : the optimal cost of the nonlinear problem with singular perturbations with state equation −εz″(t)−f(z(t))=υ and z(0)=z(T)=0 and with cost Jε (υ,z)=$\frac{1}{2r}$ ‖z−zd ‖2r L2r (0,T) +½N‖υ‖2 L2 (0,T) . We make a formal expansion of the optimality system. In the case without constraints, we introduce boundary layer terms to approximate it to order 0(εk ) for any k>0. We show that the boundary layer terms decay exponentially. We deduce, from the approximate optimality system, the expansion of jε , to order O(ε2k ) and the associated control.
DOI: 10.3233/ASY-1989-2204
Citation: Asymptotic Analysis, vol. 2, no. 2, pp. 161-177, 1989
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