Geodesic
Global solutions of the equations of elastodynamics for incompressible materials
Electronic research announcements of the American Mathematical Society, Tome 02 (1996) no. 1, pp. 50-59.

Voir la notice de l'article provenant de la source American Mathematical Society

The equations of the dynamics of an elastic material are a non-linear hyperbolic system whose unknowns are functions of space and time. If the material is incompressible, the system has an additional pseudo-differential term. We prove that such a system has global (classical) solutions if the initial data are small. This contrasts with the case of compressible materials for which F. John has shown that such solutions may not exist even for arbitrarily small data. 
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Ebin, David. Global solutions of the equations of elastodynamics for incompressible materials. Electronic research announcements of the American Mathematical Society, Tome 02 (1996) no. 1, pp. 50-59. doi : 10.1090/S1079-6762-96-00006-6. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-96-00006-6/

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