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Article type: Research Article
Authors: Baklouti, Hamadi | Mnif, Maher
Affiliations: Département de Maths, Faculté des Sciences de Sfax, 3038 Sfax, Tunisie E-mail: [email protected] | Département de Maths, I.P.E.I. Sfax, B.P. 805, 3000 Sfax, Tunisie E-mail: [email protected]
Abstract: We study the resonances of semi-classical Schrödinger operator in the one-dimensional case. We consider potential with a degenerate maximum of quartic type. We first get a precise asymptotic expansion of the scattering matrix. Then we give the asymptotic expansion of resonances near the barrier maximum outside a ball of radius 𝒪(h4/3). Finally we describe the asymptotic expansion of resonances inside the ball. Résumé. Nous étudions les résonances de l'opérateur de Schrödinger semi-classique à une variable. Nous considérons le cas d'un potentiel présentant un maximum dégénéré de type quartique. Nous obtenons une asymptotique précise de la matrice de scattering. Nous donnons aussi l'asymptotique des résonances proche du sommet de la barrière mais restant en dehors d'un disque de rayon 𝒪(h4/3). Nous décrivons enfin le développement asymptotique des résonances à l'intérieur du disque.
Journal: Asymptotic Analysis, vol. 47, no. 1-2, pp. 19-48, 2006
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