Well-posedness and Stabiliy result of Petrovsky equation with a nonlinear strong damping and delay term
Abstract
In this paper we consider a nonlinear Petrovsky equation in a bounded domain with a delay term and a strong dissipation align* utt + 2 u -μ1g1( ( ut(x,t))) -μ2g2( (ut(x,t-τ))) =0. align* We prove the existence of global solutions in suitable Sobolev spaces by using the energy method combined with Faedo-Galarkin method under condition on the weight of the delay term in the feedback and the weight of the term without delay. Furthermore, we study general stability estimates by using some properties of convex functions.
0