4n−2阶发展方程的算子半群

针对高价发展方程的形式解，将二阶发展方程扩展为时滞分布参数系统标准型中的4n−2阶发展方程，同时构造内积形成4n−2维Hilbert空间。将4n−2阶发展方程转化为一阶发展方程组，求得4n−2阶发展方程的生成算子和在一定的条件下生成半群。构造出半群的结构式并证明其具有的基本特征。当n=1时为二阶发展方程型的Golstein算子半群。
关 键 词 半群; 生成算子; Hilbert空间; 时滞分布参数系统

Abstract In allusion to the form solution to high order evolution equation, 4n−2 order evolution equation that is one of the best important standard type about time-delay distributed parameter system expand from two order evolution equation and construct the inner product to become 4n−2 dimension Halberd space at the same time. The generating operator of 4n−2 order evolution equation is obtained and it generates a semigroup when 4n−2 order evolution equation is changed into one order evolution equation set. The configuration form’s semigroup is constructed and it’s basic character is proved. In particular, the semigroup(n=1) intitules Golstein’s .
Key words semigroup; generating operator; Halberd space; time-delay distributed parameter system