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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: Robbiano, L.
Article Type: Research Article
Abstract: Dans cet article, on donne une estimation de l'énergie du contrôle de la solution d'un problème hyperbolique. Cette estimation est de la forme eC/ε2 si ε est le maximum de la norme de la solution à l'instant T.
DOI: 10.3233/ASY-1995-10201
Citation: Asymptotic Analysis, vol. 10, no. 2, pp. 95-115, 1995
Authors: Corli, Andrea
Article Type: Research Article
Abstract: We consider in this paper a strictly hyperbolic system of conservation laws, in one space dimension. We suppose that a shock wave solution to this system is given and superimpose to it small amplitude fast oscillations. These oscillations are described by sets of phase functions, and resonances are taken into account. We justify the asymptotic expansions given by the weakly non-linear geometric optics: the oscillating part of the perturbed solution is approximated by an almost periodic function (a profile) which is solution to a non-linear integro-differential mixed problem. We give at the same time an asymptotics to the shock front.
DOI: 10.3233/ASY-1995-10202
Citation: Asymptotic Analysis, vol. 10, no. 2, pp. 117-172, 1995
Authors: Nochetto, R.H. | Paolini, M. | Verdi, C.
Article Type: Research Article
Abstract: A singularly perturbed double obstacle problem is examined as a variational tool for the approximation of the geometric motion of fronts. The relaxation parameter is space-time dependent, thereby allowing the control of transition layer thickness and related interface pointwise accuracy. Optimal order interface error estimates are derived for smooth evolutions. The estimates have a local character for small time, namely they depend on the relaxation parameter local magnitude. The proof is based on constructing suitable sub and supersolutions, which incorporate a number of shape corrections to the basic standing wave profile, and using a modified distance function to the front. …Numerical simulations illustrate how the variable transition layer thickness can be exploited in dealing with large curvatures and ultimately in resolving singularities. Show more
DOI: 10.3233/ASY-1995-10203
Citation: Asymptotic Analysis, vol. 10, no. 2, pp. 173-198, 1995
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