无限维空间上的波方程和 Schrodinger方程解的存在和唯一性

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

摘要:

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

Abstract:

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 and Schrodinger equations are obtained by the semigroup method.