Long-time behavior of a suspension bridge equations with past history

摘要

In this paper, we study a suspension bridge equation with memory effects. For the suspension bridge equation without memory, there are many classical results. Existing results mainly devoted to existence and uniqueness of a weak solution, energy decay of solution and existence of global attractors. However the existence of global attractors for the suspension bridge equation with memory was no yet considered. The object of the present paper is to provide some results on the well-posedness and long-time behavior to the suspension bridge equation when the unique damping mechanism is given by the memory term.