Stability of the Kawahara equation with time-varying delay

In this work, we consider the nonlinear Kawahara equation with internal time-dependent delay in a bounded domain. We prove that this equation has a unique solution. Moreover, we use a Lyapunov functional approach to prove the exponential stability of the nonlinear system, under some assumptions on the weights of the feedbacks and on the time-dependent delay. We present some numerical simulations to illustrate the obtained results.

کلیدواژه ها:

Exponential stability ، internal feedback with delay ، energy of the system ، Lyapunov functional