Long-time behavior of a model of extensible beams with nonlinear boundary dissipations

This paper is concerned with the long-time behavior of a model of extensible beams utt+uxxxx−M(∫0L|ux|2dx)uxx=h, defined in a bounded interval (0,L)(0,L), where MM is a continuous nonnegative function and hh is a static load. To this problem little is known with nonlinear boundary conditions. One considers the case where a nonlinear forcing interacts with the shear force at the boundary. Then the existence of a global attractor is proved with a sole boundary damping.