Stability analysis for Kawahara equation with boundary time-varying delay

Abstract

This paper deals with the stability of the (generalized) Kawahara equation with a time-varying delay on the boundary feedback. First, we demonstrate the well-posedness of the nonlinear Kawahara system by using semigroup theory and fixed-point arguments. Next, we establish the exponential stability of this equation by imposing conditions on the length of the spatial domain and the time-varying delay. Specifically, this result is achieved by introducing a suitable energy function and using the Lyapunov approach to ensure that the unique solution of the system decays exponentially. Finally, we present some conclusions.