Global solution and asymptotic behavior for the variable coefficient beam equation with nonlinear damping

Abstract

This paper is concerned with the initial-boundary value problem for a variable coefficient beam equation with nonlinear damping. Such a model arises from the vertical deflections of a damped extensible elastic inhomogeneous beam whose density depends on time and position. By using the Faedo-Galerkin method and energy method, we obtain the existence and uniqueness of global strong solution. Furthermore, the exponential decay estimate for the total energy is also derived.