On The Initial-boundary Value Problem For The Nonlinear Partial Differential Equation With Integral Term

Integro-differential equations are topic problem in recent years, especially, those form viscoelastic mechanics are focused on by researchers. In this paper, we just consider the problem that finite viscoelastic beam vibrates along the axis direction ,that is to say, we study the existence and uniqueness of the global strongly solution of the following initial-boundary value problem for the nonlinear integro-differential equationAt the same time, the existence of the global classical solution is considered.To begin with, by using the theory of Volterra Integral equations, the problem (1)-(3) are equivalent to the following initial boundary value problem...