【摘要】 研究比较一般的阻尼波动方程 :ψ″ -Δψ +kψt =0。证明了在时间足够长而阻尼足够小的情况下可以通过控制边界上某一部分的振动过程使得整个区域内的波动系统在某种正则空间内从任意初始状态出发到达任意终止状态。证明过程主要思路是HUM方法即先构造对偶系统 :″-Δ -kt =0 并证明其边界法向连续能观 ,再将其边界法向导数作为控制加在阻尼控制系统的边界上以实现精确能控更多还原

【Abstract】 Wave equation with damp:ψ″-Δψ+kψ t=0 is studied. This system can be driven from any initial state to any terminal state in proper space,if the time interval is long enough and the damp is small enough.The proof is based on the Hilbert Uniqueness Method,i.e.,to verify the continuous observability of the dual system: ″-Δ-k t=0 by its boundarynormal derivative and then put the normal derivative onto the damped system as boundary control.更多还原