A note on time decay for the nonlinear beam equation

In this note we obtain another form of Morawetz-type identity by Lagrange method and present a simple proof of the time decay estimates for the solution of the nonlinear beam equation, for a nonlinear term with repelling sign, as t→∞. As an immediate consequence, we also get the timeintegrability of the local energy of the solution for the beam equation.  2005 Elsevier Inc. All rights reserved