考察了带有满足全局Lipschitz条件的非线性项的抛物系统在有界状态域上的精确能控制性问题。当目标状态限制于H^2(Ω)时,证明了该抛物非线性系统是精确能控的。证明过程主要运用了Schauder不动点方法。
The semilinear heat equation involving globally Lipschitz nonlinearities in a bounded domain of Rn is studied. The system is proved to be exact controllable when the terminal state belongs to the Sobolev space of functions having two square integrable derivatives. The proof uses a variant of a classical Schauder's fixed point method.