一类非线性波的能量衰减

The Energy Decay of a Nonlinear Wave System

考虑由初边值混合问题描述的一类非线性波动系统，并给出几个有意义的结果．此系统被描述为适当的Ｈｉｌｂｅｒｔ空间中的发展方程，运用泛函分析及算子半群方法讨论了相应发展方程主算子的谱特征及半群性质，最后证明了所考虑的非线性波系统的能量是按指数规律衰减的．

A nonlinear wave system described as a mixed initial-boundary value problem was investigated in the present paper,and the some more meaningful results were obtained. The considered system can be formulated as an evolution equation in an appropriate Hilbert space, and the some spectral properties and semigroups properties of the main operator corresponding to the evolution equation were discussed by means of functional analysis and operators semigroup. Finally,an important result that the energy of the system is exponential decay was proved.