一类退化抛物方程边界控制问题的近似可控性

Approximate Controllability of Boundary Control Problems for a Class of Degenerate Parabolic Equations

用共轭方程的Carleman估计研究退化抛物方程的边界控制问题,得到了该问题的近似可控性.结果表明:对任意一个目标函数,均存在一个控制函数,使问题的解在有限时间内可以充分接近目标函数.

By using Carleman estimates of the adjoint equations,we investigated the boundary control problem of degenerate parabolic equations,and obtained its approximate controllability.The result shows that for any objective function,there exists a control function such that the solution of the problem can be fully close to the objective function in a finite time.