針對(duì)高價(jià)發(fā)展方程的形式解，將二階發(fā)展方程擴(kuò)展為時(shí)滯分布參數(shù)系統(tǒng)標(biāo)準(zhǔn)型中的4n?2階發(fā)展方程，同時(shí)構(gòu)造內(nèi)積形成4n?2維Hilbert空間。將4n?2階發(fā)展方程轉(zhuǎn)化為一階發(fā)展方程組，求得4n?2階發(fā)展方程的生成算子和在一定的條件下生成半群。構(gòu)造出半群的結(jié)構(gòu)式并證明其具有的基本特征。當(dāng)n=1時(shí)為二階發(fā)展方程型的Golstein算子半群。
關(guān) 鍵 詞 半群; 生成算子; Hilbert空間; 時(shí)滯分布參數(shù)系統(tǒng)

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