Regularity result for the problem of vibrations of a nonlinear beam. (English) Zbl 1137.74027

M’Bengue, M’Bagne F.; Shillor, Meir

Electron. J. Differ. Equ. 2008, Paper No. 27, 12 p. (2008).

Summary: We study a model for the dynamics of Gao nonlinear beam, which allows for buckling. Existence and uniqueness of local weak solution was established earlier. In this work the further regularity in time of the weak solution is shown using recent results on evolution problems. Moreover, the weak solution is shown to be global, existing on each finite time interval.

MSC:

74H45	Vibrations in dynamical problems in solid mechanics
74H30	Regularity of solutions of dynamical problems in solid mechanics
74K10	Rods (beams, columns, shafts, arches, rings, etc.)

Keywords:

energy balance; pseudomonotone operators; global weak solution