Outdated Archival Version

These pages are not updated anymore. They reflect the state of 20 August 2005. For the current production of this journal, please refer to http://www.math.psu.edu/era/.

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/

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.

Copyright American Mathematical Society 1996

TeX source (32K)
DVI (46K)
PostScript (144K)

Article Info

• ERA Amer. Math. Soc. 02 (1996), pp. 50-59
• Publisher Identifier: S 1079-6762(96)00006-5
• 1991 Mathematics Subject Classification. Primary 35L70, 35Q72, 73C50, 73D35
• Key words and phrases. Non-linear hyperbolic, elastodynamics, incompressible, global existence
• Received by the editors December 29, 1995
• Communicated by James Glimm
• Comments (When Available)

David G. Ebin

SUNY at Stony Brook, NY 11794-3651

E-mail address: ebin@math.sunysb.edu

Partially supported by NSF grant DMS 9304403