## Differential and Integral Equations

### Rates of decay of a nonlocal beam equation

#### Abstract

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.

#### Article information

Source
Differential Integral Equations, Volume 10, Number 6 (1997), 1075-1092.

Dates
First available in Project Euclid: 1 May 2013