Global Classical Solutions of IBVP to Nonlinear Equation of a Suspended String

Abstract

We are concerned with the existence and uniqueness of the \textit{classical} solution to IBVP for a nonlinear equation of a suspended string with uniform density to which a monotonous nonlinear time-independent outer force works. For this purpose we derive the higher order energy estimates, and employ the Galerkin method combining with the compactness argument along the refined method of [Sath]. We need the regularity theory of Nirenberg type for the suspended string operator $L$.