Nonlocal approach to problems on longitudinal vibration in a short bar

Abstract

In this article, we consider a problem with dynamic nonlocal conditions for a forth-order PDE with dominating mixed derivative. This problem is closely related to vibration problems, in particular, to longitudinal vibration in a short bar. The existence and uniqueness of a generalized solution are proved.

Keywords

• Nonlocal problem
• longitudinal vibration
• forth order equation
• dynamical boundary condition
• generalized solution