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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: Bardi, Martino | Perthame, Benoît
Article Type: Research Article
Abstract: Let u be any smooth solution of −εaij uxi xj +aij uxi uxj +bi uxi =εc in B1 ={x:|x|<1}, where ε is a small parameter. We prove some uniform estimates on u in W1,q under weak assumptions on the coefficients aij , bi and c. This is motivated by the study of exponential behaviors for solutions of linear elliptic equations −εaij vxi xj +bi vxi +cv=0, as ε goes to 0. For this equation, our result provides an estimate of Harnack type sup Br v≤Cinf Br v, with C=e−krα /ε for …some α≤1. Show more
DOI: 10.3233/ASY-1991-4101
Citation: Asymptotic Analysis, vol. 4, no. 1, pp. 1-16, 1991
Authors: Frank, L.S. | Norde, H.W.
Article Type: Research Article
Abstract: Initial-boundary value problems for the linearized Korteweg-de Vries equation with a small dispersion term are considered. Singularities of the corresponding families of the Green and Poisson operators are analysed as the small parameter vanishes. Asymptotic formulae for the eigenvalues and eigenfunctions of the corresponding singularly perturbed operator in the space variable are derived and justified. These formulae yield the conclusion that the dispersive nature of the linearized Korteweg-de Vries equation (in the case of the Cauchy problem) is preserved asymptotically for some perturbation terms in the case of mixed initial-boundary value problems too, when the small parameter goes to zero …taking some explicitly specified discrete values. Show more
DOI: 10.3233/ASY-1991-4102
Citation: Asymptotic Analysis, vol. 4, no. 1, pp. 17-59, 1991
Authors: Liess, Otto
Article Type: Research Article
Abstract: In the present paper, we study decay estimates for solutions of Maxwell's system in homogeneous anisotropic media. While the estimates are similar to related estimates for the wave equation, the main novelty comes from the fact that here we have a case of characteristics with variable multiplicity.
DOI: 10.3233/ASY-1991-4103
Citation: Asymptotic Analysis, vol. 4, no. 1, pp. 61-95, 1991
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