一类双耦合线性退化抛物方程组的近似可控性

Approximate Controllability of a Class of Double Coupled Linear Degenerate Parabolic Equations

考虑一类双耦合线性退化抛物方程组初边值问题的近似可控性,通过克服方程组退化性的困难,借助对偶问题构造出控制函数,证明了初边值问题在L2中的近似可控性.即对任意L2中的初值函数和目标函数,可找到一个L2中的控制函数,使方程组初边值问题的解在终止时刻于L2中近似可达目标函数.

We considered the approximate controllability of the initial boundary value problems of a class of double coupled linear degenerate parabolic equations.We overcame the difficulty of the degeneracy of the equations,constructed the control function by means of their conjugate problems,and proved the approximate controllability of the initial boundary value problem in L2.In other words,for any initial value function and desired function in L2,we could find a control function in L2,which made the solution of the initial boundary value problem of the equation approximately reach the desired function in L2 at the terminal time.