Stabilization results for delayed fifth-order KdV-type equation in a bounded domain

Studied here is the Kawahara equation, a fifth-order Korteweg-de Vries type with time-delayed internal feedback. Under suitable assumptions on time delay coefficients, we prove that solutions of this system are exponentially stable. First, considering damping and delayed system, some restriction spatial length domain, energy goes to $ 0 as t \rightarrow \infty $. After that, by introducing more general energies, show using Lyapunov approach, equation zero exponentially, initial data small in domain. To remove these hypotheses, use compactness-uniqueness argument which reduces our problem an observability inequality, showing semi-global stabilization result.