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Electronic Research Announcements

ISSN 1079-6762



Global solutions of the equations of elastodynamics for incompressible materials

Author: David G. Ebin
Journal: Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 50-59
MSC (1991): Primary 35L70, 35Q72, 73C50, 73D35
MathSciNet review: 1405969
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Abstract: 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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Keywords: Non-linear hyperbolic, elastodynamics, incompressible, global existence
Received by editor(s): December 29, 1995
Additional Notes: Partially supported by NSF grant DMS 9304403
Communicated by: James Glimm
Article copyright: © Copyright 1996 American Mathematical Society