**Nour-Eddine Amroun, Abbes Benaissa**

## Global Existence and Energy
Decay of Solutions to a Petrovsky Equation with General Nonlinear Dissipation
and Source Term

**Abstract:**

We consider the nonlinearly damped semilinear Petrovsky equation

$$ u''-\Delta_{x}^{2}u+g(u')=b\ u|u|^{p-2}\quad \hbox{ on }\;\;\Omega\times [0,
+\infty[ $$

and prove the global existence of its solutions by means of the stable set
method in $H_{0}^{2}(\Omega)$ combined with the Faedo-Galerkin procedure.
Furthermore, we study the asymptotic behavior of solutions when the nonlinear
dissipative term $g$ does not necessarily

have a polynomial growth near the origin.

**Keywords:**

General nonlinear dissipation, nonlinear source, global existence, decay rate,
multiplier method.

**MSC 2000:** 35L45, 93C20, 35B40, 35L70