Regularity result for the problem of vibrations of a nonlinear beam

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.

Keywords

• Nonlinear beam
• existence and uniqueness
• energy balance
• pseudomonotone operators
• regularity