Boundary feedback control of elastic beam equation with structural damping and stability

In this paper, we consider the partial differential equation of an elastic beam with structural damping by boundary feedback control. First, we prove this closed system is well-posed; then we establish the exponential stability for this elastic system by using a theorem whichbelongs to F. L. Huang^2]; finally, we discuss the distribution and multiplicity of the spectrum of this system. These results are very important and useful in practical applications.