We consider a class of abstract second order evolution equations with a restoring force that is strictly superlinear at infinity with respect to the position, and a dissipation mechanism that is strictly superlinear at infinity with respect to the velocity.

Under the assumption that the growth of the restoring force dominates the growth of the dissipation, we prove a universal bound property, namely that the energy of solutions is bounded for positive times, independently of the initial condition. Under a slightly stronger assumption, we show also a universal decay property, namely that the energy decays (as time goes to infinity) at least as a multiple of a negative power of t, again independent of the boundary conditions.

We apply the abstract results to solutions of some nonlinear wave, plate and Kirchhoff equations in a bounded domain.

我们考虑一类抽象的二阶演化方程，其恢复力在位置无穷大时绝对超线性，而耗散机制在速度无穷远时严格超线性。

在恢复力的增长主导耗散的增长的假设下，我们证明了一个普遍的束缚性质，即溶液的能量在正时有界，而与初始条件无关。在一个稍强的假设下，我们还显示出一个通用的衰减特性，即能量衰减（随着时间趋于无穷大）至少是t的负幂的倍数，而又与边界条件无关。

我们将抽象结果应用于有界域中某些非线性波，板和Kirchhoff方程的解。