Semigroup well-posedness and exponential stability for the von Kármán beam equation under the combined boundary control of nonlinear delays and non-delays

Abstract

This paper considers the stabilization problem of the von Kármán beam equation with a combined boundary control of nonlinear delays and nonlinear non-delays. The combined boundary controls are applied at the transverse and longitudinal boundaries of the von Kármán beam, respectively. In this paper the nonlinear semigroup method is adopted in the investigation for the establishment of the well-posedness of the resulting closed-loop system. Constructing an appropriate energy-like function, the exponential decay rate of energy of the closed-loop system is demonstrated by a generalized Gronwall-type integral inequality and the integral multiplier technique.