Some qualitative properties for the equations of pre-stressed viscoelastic solids

In this paper, we study the qualitative behavior of a fifth order scalar partial differential equation arising in the framework of the small amplitude motion approximation for pre-stressed non-linear viscoelastic materials of first grade. We establish existence, uniqueness, regularity and exponential decay of the solutions. Moreover, we study the role of the various constitutive inequalities in the stability and instability of the solutions.