论文标题
局部耦合波方程的确切可控性和稳定性：理论结果
Exact controllability and stabilization of locally coupled wave equations : theoretical results
论文作者
论文摘要
在本文中，我们研究了一个仅由一个方程起作用的内部局部控制的速度，由速度结合的两个波方程的系统的确切可控性和稳定性。我们区分了两个案例。在第一个时，当波以相同的速度传播时：使用频域方法与乘数技术结合使用，我们证明当耦合区域满足几何控制条件GCC时，系统是指数稳定的。根据Haraux（[11]）的结果，我们建立了主要的间接可观察性不平等。通过嗡嗡声方法导致该结果证明总系统可以通过局部分布式控制完全控制。在第二种情况下，当波以不同的速度传播时，我们在弱的能量空间中建立了指数衰减率。因此，使用[11]的结果完全可以控制系统。
In this paper, we study the exact controllability and stabilization of a system of two wave equations coupled by velocities with an internal, local control acting on only one equation. We distinguish two cases. In the first one, when the waves propagate at the same speed: using a frequency domain approach combined with multiplier technique, we prove that the system is exponentially stable when the coupling region satisfies the geometric control condition GCC. Following a result of Haraux ([11]), we establish the main indirect observability inequality. This results leads, by the HUM method, to prove that the total system is exactly controllable by means of locally distributed control. In the second case, when the waves propagate at different speed, we establish an exponential decay rate in the weak energy space. Consequently, the system is exactly controllable using a result of [11].
