二阶积分偏微分方程的剩余可控性

Controllability to Rest of the Second Order Integro-Differential Equation

不同于线性偏微分方程,积分偏微分方程的零能控性与剩余可控性之间关联不大。利用儒歇定理、拉普拉斯变换等方法分别得到具有三种常用积分核的二阶积分偏微分方程的非剩余可控性。这类结果是对积分偏微分方程能控性的补充。

Unlike linear partial differential equations, the null controllability of integro-differential equations is not related to controllability to rest. Using Rouché’s theorem, Laplace transform and so on, we obtain that second order integro-differential equations with three common integral kernels which cannot be controlled to rest, respectively. This result is a supplement to the controllability of integro-differential equations.