LAUSR

In this article, we consider a nonlinear damped Petrovsky equation in bounded domain. The nonlinear damping is effective only in a neighborhood of a suitable subset of the boundary. The well‐posedness and regularity of solution is discussed owing to the nonlinear semigroup theory together with the Faedo–Galerkin approach. By energy method combined with the piecewise multiplied method and relying on the localized smoothing property, we show the exponential and polynomial stabilities by discussing with respect to the parameter p.