On exponential stabilization of a nonlinear neutral wave equation

Abstract

This work aims to study a nonlinear wave equation subject to a delay of neutral type. The nonlinearity and the delay appear in the second time derivative. In spite of the fact that delays by nature, have an instability effect on the structures, the strong damping is sufficient to allow the system to reach its equilibrium state with an exponential manner. The difficulties arising from the nonlinearity have been overcome by using an inequality due to a Sobolev embedding theorem. The main result has been established without any condition on the coefficient of the neutral delay.