无限维空间上的波方程和Schrodinger方程解的存在性和唯一性

Existence and uniqueness of solutions of wave equation and Schrodinger equation in infinite dimension

本文首先在无限维空间上定义了椭圆方程的弱解并得到其存在性和唯一性,然后以此为基础在一定的条件下利用半群方法得到了无限维空间上的波方程和Schr dinger方程解的存在性与唯一性.

In this paper,we define the weak solutions of the elliptic equation in infinite dimension and obtain their existence and uniqueness.Then under suitable assumptions,the existence and uniqueness of solutions of the infinite dimensional wave equation and Schr dinger equation are obtained by the semigroup method.