in the study of semigroup theory . a very basic problem is that what kind of the semigroup's property we can get from its idempotent's property 在半群代數(shù)理論中,一個(gè)非?;镜膯栴}是,從半群的冪等元的性質(zhì)可以得到該半群的何種性質(zhì)
some conditions are obtained by using the semigroup theory, the properties of nonnegative matrices and the techniques of inequalities to determine the asymptotically stable region of the equilibrium 通過半群理論、非負(fù)矩陣性質(zhì)和不等式技巧,得到估計(jì)這類方程平衡態(tài)漸近穩(wěn)定域的方法。
by using the operator semigroup theory we prore the existence of a unique positive solution of this model on c0 and study the spectral properties of the corresponding operator 我們運(yùn)用算子半群理論,證明了此模型在序列空間c。上存在唯一非負(fù)的時(shí)間依賴解,并且研究了相應(yīng)算子的譜特征。
2 ) the stability of travelling wave solutions by analytic semigroup theory and a detailed spectral analysis, the asymptotic stability of the travelling waves we obtained above is proved 2)行波的穩(wěn)定性在解析半群框架下,利用譜分析的方法,本文得到以上行波的局部漸近穩(wěn)定性,而在此以前一直未有這方面的詳細(xì)結(jié)果。
the global existence of solution to the initial-boundary value problem of a nonlinear fourth-order wave equation with a damping term and a force source term was proved based on the standard semigroup theory and by introducing a modified energy function 摘要根據(jù)半群理論,引進(jìn)修改的能量函數(shù),證明了具有阻尼項(xiàng)和力源項(xiàng)的四階波動(dòng)方程的初邊值問題解的整體存在性。