We consider a nonlinear Petrovsky equation in a bounded domain with a strong dissipation, and prove the existence and the uniqueness of the solution using the energy method combined with the Faedo-Galerkin procedure under certain assumptions. Furthermore, we study the asymptotic behaviour of the solutions using a perturbed energy method.
This work deals with a logarithmic Petrovsky equation with delay term. Under appropriate conditions, we prove the blow up of solutions in a finite time in a bounded domain. Our results are more general than the earlier results.
Well-posedness and general energy decay of solutions for a Petrovsky equation with a nonlinear strong dissipation