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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: Esteban, M.J. | Lions, P.L.
Article Type: Research Article
Abstract: It was already known that when the topological charge k is larger than 1, the ground state energy for Skyrme's problem can never be achieved by a hedge-hog type function. In this paper we prove that in fact the ratio of the ground state energy to the lower bound of the energy for the hedge-hog functions converges to 0 as k−1 .
DOI: 10.3233/ASY-1988-1301
Citation: Asymptotic Analysis, vol. 1, no. 3, pp. 187-192, 1988
Authors: Brüning, Jochen | Schröder, Herbert
Article Type: Research Article
Abstract: The classical result of Minakshisundaram and Pleijel on the asymptotic expansion of the trace of the heat semigroup associated with the Laplacean on a compact Riemannian manifold M has been generalized by Brüning and Heintze to the case that a compact group is acting on M by isometries. They obtained an asymptotic expansion involving logarithmic terms. Here we prove that these terms vanish if M has constant sectional curvature or if M is a warped product M=[0,π]×f Sn with n≥2 and suitable f.
DOI: 10.3233/ASY-1988-1302
Citation: Asymptotic Analysis, vol. 1, no. 3, pp. 193-203, 1988
Authors: Tatsien, Li | Qi, Tang
Article Type: Research Article
Abstract: In this paper we present and discuss a class of problems of boundary homogenization for parabolic equations, and point out its application to the heat analysis of a car wheel.
DOI: 10.3233/ASY-1988-1303
Citation: Asymptotic Analysis, vol. 1, no. 3, pp. 205-212, 1988
Authors: Penzel, F.
Article Type: Research Article
Abstract: The asymptotical behaviour of the solution of (n×n)-systems of singular integral equations with piecewise Hoelder-continuous coefficients is described, even if the explicit solution is not known.
DOI: 10.3233/ASY-1988-1304
Citation: Asymptotic Analysis, vol. 1, no. 3, pp. 213-225, 1988
Authors: Charbonnel, Anne-Marie
Article Type: Research Article
Abstract: We consider ν pseudodifferential operators, Q1 (h),…,Qν (h), acting in Rn , commuting together, depending on a small parameter h. For instance, one of them is the Schrödinger operator with a potential V(x) satisfying the condition $\underline{lim}_{|x|\rightarrow +\infty}V(x)>E$ . Under suitable conditions, we establish a functional ca1culus to define f(Q1 (h),…,Qν (h)) as a pseudodifferential operator of the same type, when f belongs to C∞ 0 (Rν ). We use it to study the semiclassical behaviour of the joint spectrum of Q1 (h),…,Qν (h), lying in a compact of Rν where it is discrete. When these operators form …a quantically integrable system, we give more precise estimations. Our results generalize those obtained by Helffer and Robert for one operator acting in Rn . Show more
DOI: 10.3233/ASY-1988-1305
Citation: Asymptotic Analysis, vol. 1, no. 3, pp. 227-261, 1988
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