## Differential and Integral Equations

### Time behavior for a class of nonlinear beam equations

#### Abstract

We consider a class of nonlinear beam equations in the whole space $\mathbb R^n$. Using previous important work due to Levandovsky and Strauss we prove that, locally, the $H^1$-norm of a strong solution approaches zero as $t \to +\infty$ as long as the spatial dimension $n \ge 6$. The problem remains open for dimensions $1 \le n \le 5$.

#### Article information

Source
Differential Integral Equations, Volume 19, Number 1 (2006), 15-29.

Dates
First available in Project Euclid: 21 December 2012