Electron. J. Diff. Eqns., Vol. 2008(2008), No. 27, pp. 1-12.

Regularity result for the problem of vibrations of a nonlinear beam

M'Bagne F. M'Bengue, Meir Shillor

Abstract:
A model for the dynamics of the Gao nonlinear beam, which allows for buckling, is studied. Existence and uniqueness of the local weak solution was established in Andrews et al. (2008). In this work the further regularity in time of the weak solution is shown using recent results for evolution problems. Moreover, the weak solution is shown to be global, existing on each finite time interval.

Submitted January 25, 2008. Published February 28, 2008.
Math Subject Classifications: 74H30, 35L75, 74K10, 74D10, 74H45.
Key Words: Nonlinear beam; existence and uniqueness; energy balance; pseudomonotone operators; regularity.

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M'Bagne F. M'Bengue
Department of Mathematics and Statistics
Oakland University
Rochester, MI 48309, USA
email: mfmbengu@oakland.edu
Meir Shillor
Department of Mathematics and Statistics
Oakland University
Rochester, MI 48309, USA
email: shillor@oakland.edu

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