We consider a beam equation with a nonlocal nonlinearity of Kirchhoff type on an unbounded domain. We show that smooth global solutions decay (in time) at a uniform rate as $t\to +\infty$. Our model is closely related to a nonlinear Schrödinger equation with a time-dependent dissipation. We use this observation to obtain intermediate information on our original model.
"Rates of decay of a nonlocal beam equation." Differential Integral Equations 10 (6) 1075 - 1092, 1997. https://doi.org/10.57262/die/1367438220