In this paper, we investigate a one-dimensional thermoelastic Bresse system, where the heat conduction is given by Green and Naghdi theories. Under some assumptions on the memory kernel and a new introduced stability number, we prove that the unique damping given by the memory term is sufficiently strong to stabilize the system exponentially. In fact, we establish a general decay result from which the exponential and polynomial decays are only special cases.
Starting with the Naghdi model for a shell in Cartesian coordinates, we derive a model for the contact of this shell with a rigid body. We also prove the well-posedness of the resulting system of variational inequalities.Résumé À partir du modèle de Naghdi pour une coque en coordonnées cartésiennes, nous proposons un modèle décrivant le contact de cette coque avec un corps rigide. Nous prouvons que le système d'inéquations variationnelles qui en résulte est bien posé.
In this study we considered a deformed elastic solid with a unilateral contact of a rigid body. We studied the existence, uniqueness and continuity of the deformation of this solid with respect to the data. We proved the existence of solutions for a class of variational inequalities.
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