Asymptotic Analysis - Volume 15, issue 1

Authors: Korotyaev, Evgeni

Article Type: Research Article

Abstract: Asymptotic estimates at large time of the Green function to the wave equation with periodic coefficients are found. An estimate of the wave front is also obtained. It is shown that the spectral band (with number n=0,1,2,…) of the corresponding Hill operator ‘creates’ a wave having the front velocity cn < 1 . Estimates of cn in the terms of the gap lengths, the effective masses of the Hill operator are proved, both with fixed number n and their sums. Some extensions for more general cases (the Dirac operator with periodic coefficients, the Schrodinger operator with finite band …potentials etc.) are also obtained. Show more

DOI: 10.3233/ASY-1997-15101

Citation: Asymptotic Analysis, vol. 15, no. 1, pp. 1-24, 1997

Authors: Barucq, H. | Hanouzet, B.

Article Type: Research Article

Abstract: We develop an asymptotic study of Maxwell's system involving an absorbing boundary condition. First- and second-order systems are considered. In both cases, we prove that the solution converges towards a steady state depending on the geometrical properties of the obstacle. The asymptotic state involves the data of the problem.

Keywords: Maxwell's system, absorbing boundary conditions, asymptotic behaviour, electromagnetic waves

DOI: 10.3233/ASY-1997-15102

Citation: Asymptotic Analysis, vol. 15, no. 1, pp. 25-40, 1997

Authors: Berthier, Michel | Loray, Frank

Article Type: Research Article

DOI: 10.3233/ASY-1997-15103

Citation: Asymptotic Analysis, vol. 15, no. 1, pp. 41-54, 1997

Authors: Klopp, Frédéric

Article Type: Research Article

Abstract: Sous l'hypothèse V périodique, on étudie dans le cadre de la limite semi-classique (h→0), le spectre de l'opérateur Pt =−h2 Δ+V+tδV agissant sur L2 (Rn ), où t est une constante de couplage positive et δV est une fonction localisée au voisinage de m puits distincts de V. Pour ce faire, on ramène par équivalence unitaire l'étude de l'opérateur Pt à celle d'un noyau de Birman–Schwinger. Cette réduction nous permet alors de montrer l'existence de valeurs propres pour Pt quand |t| n'est pas trop petit (ceci dépendant de la dimension n). Puis on étudie le comportement de ces …valeurs propres en fonction de |t| et de la localisation des m puits de V que l'on a perturbé. Show more

Keywords: Opérateurs de Schrödinger, limite semi-classique, potentiels périodiques, localisation de fonctions propres

DOI: 10.3233/ASY-1997-15104

Citation: Asymptotic Analysis, vol. 15, no. 1, pp. 55-102, 1997