阻尼Schrodinger方程和板方程解的能量指数衰减

Exponential decay of energy for the solutions to the damped Schrodinger and plate equations

研究了阻尼Schrodinger方程和板方程在有界区域上的能量衰减。在边界阻尼控制下,利用乘子技术和算子半群理论,分别建立了Schrodinger方程和板方程的能量估计不等式,证明了这两个系统解的能量是指数衰减的,推广了已有的相关结果。

The energy decay of the damped Schrodinger and plate equations in bounded domain are studied. Under the boundary damping conditions, by using multiplier techniques and operator semigroup theory, the energy estimation inequalities of Schrodinger and plate equations are established respectively. It proves that the energy of the solutions to the two systems decay exponentially, which extends the existing related results.