Uniqueness and continuous dependence on the initial data for a class of non-linear shallow shell problems

John Cagnol; Irena Lasiecka; Catherine Lebiedzik; Richard Marchand

doi:10.1016/j.crma.2006.02.034

Mathematical Problems in Mechanics

Uniqueness and continuous dependence on the initial data for a class of non-linear shallow shell problems
[Théorème d'unicité et de dépendence continue des solutions par rapport aux conditions initiales pour une classe de problèmes non linéaires de coques peu profondes]

Présenté par : Philippe G. Ciarlet

John Cagnol ¹ ; Irena Lasiecka ² ; Catherine Lebiedzik ³ ; Richard Marchand ⁴

¹ Pôle universitaire Leonard-de-Vinci, ESILV, DER CS, 92916 Paris La Défense cedex, France
² University of Virginia, Department of Mathematics, Kerchof Hall, P.O. Box 400137, Charlottesville, VA 22904, USA
³ Wayne State University, Department of Mathematics, 656 W. Kirby, Room 1150, Detroit, MI 48202, USA
⁴ Slippery Rock University, Department of Mathematics, 229 Vincent Science Hall, Slippery Rock, PA 16057, USA

Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 711-716.

Résumé
Abstract

Dans cette Note, nous nous intéressons au modèle introduit en 1966 par W.T. Koiter, puis étudié par M. Bernadou et J.T. Oden. Nous démontrons l'unicité de la solution du modèle dynamique et que cette solution est continue par rapport aux conditions initiales.

This note is concerned with the non-linear shallow shell model introduced in 1966 by W.T. Koiter, and later studied by M. Bernadou and J.T. Oden. We show the uniqueness of the solution to the dynamical model and that this solution is continuous with respect to the initial data.

Reçu le : 2006-01-31
Accepté le : 2006-02-10
Publié le : 2006-03-24

DOI : 10.1016/j.crma.2006.02.034

Affiliations des auteurs :

John Cagnol ¹ ; Irena Lasiecka ² ; Catherine Lebiedzik ³ ; Richard Marchand ⁴

¹ Pôle universitaire Leonard-de-Vinci, ESILV, DER CS, 92916 Paris La Défense cedex, France
² University of Virginia, Department of Mathematics, Kerchof Hall, P.O. Box 400137, Charlottesville, VA 22904, USA
³ Wayne State University, Department of Mathematics, 656 W. Kirby, Room 1150, Detroit, MI 48202, USA
⁴ Slippery Rock University, Department of Mathematics, 229 Vincent Science Hall, Slippery Rock, PA 16057, USA

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     title = {Uniqueness and continuous dependence on the initial data for a class of non-linear shallow shell problems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {711--716},
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John Cagnol; Irena Lasiecka; Catherine Lebiedzik; Richard Marchand. Uniqueness and continuous dependence on the initial data for a class of non-linear shallow shell problems. Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 711-716. doi : 10.1016/j.crma.2006.02.034. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.02.034/

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