拟Galerkin逼近方程及应用

Quasi-Galerkin Approximating Equation and Its Application

仿照Ｇａｌｅｒｋｉｎ逼近方法：Ｘｎ是Ｘ的ｎ维线性子空间，Ｐｎ：Ｘ→Ｘｎ为投影算子（Ｉ＋ＫｎＦｎ）Ｘｎ＝Ｐ＊ｎｙ其中Ｐ＊ｎ为Ｐｎ的共轭算子，Ｋｎ＝Ｐ＊ｎＫＰｎ，Ｆｎ＝ＰｎＦＰ＊ｎ．建立了一种新的不同的Ｇａｌｅｒｋｉｎ逼近方程，并证明了一类非线性算子方程在此逼近意义下是可解的。

Following Galerkin approximating method, X n is X′s n dimensional linear sub-space, and P n:X→X n is the projection operator (I+K nF n)X n=P * ny where P * n is the conjugate operator to P n, consequently K n=P * nKP n, F n=P nFP * n, hence, a new kind of different Galerkin approximating equation is established. Thereafter, the paper proves that a sort of nonlinear operator equations is solvable under the approximating implication.