空间 R~n 中一类矩量半群

给出了空间Ｒｎ中正则集的定义，在Ｒｎ空间中的正则紧凸集上，研究并得到了生成矩量半群的五个彼此等价的条件，这些结果推广了ＨＢｕｃｈｗａｌｔｅｒ和ＧＣａｓｓｉｅｒ的工作     

左阿基米德序半群的自然序带

刻划了分别可分解为左阿基米德序半群，左单序半群的幂零拆张序半群和左单序半群的自然序带的序半群的特征。     

Semigroup generation and stabilization by A-bounded feedback perturbations

Let A be a generator of a strongly continuous semigroup of operators, and assume that C and H are operators such that A + CH generates a strongly continuous semigroup S_H(t) on X. Let λ₀ be a real number in the resolvent set of A, and let ε [−1, 1]. Then there are some fairly unrestrictive conditions under which A+(λ₀ − A)CH(λ₀ − A)⁻ also generates a strongly continuous semigroup S_K(t) on X which has the same exponential growth rate as S_H(t). Given an input operator B, we can use this to identify a class of feedback perturbations K such that A + BK generates a strongly continuous semigroup. We can also use this result to identify classes of feedbacks which can and cannot uniformly stabilize a system. For example, we show that if the control on a cantilever beam in the state space H₀²[0, 1] × L²[0, 1] is a moment force on the free end, then we cannot stabilize the beam with an A^−1/2-bounded feedback, but we can find an A^−1/4-bounded feedback, for any > 0, which does stabilize the beam.     

热—板传输系统的稳定性分析

本文研究由处于相邻区域的板方程和热方程构成的耦合系统的稳定性质, 其中耦合来自两个区域的交界 面上的传输边界条件. 在该传输系统中, 热方程起着控制器的作用, 且耗散通过交界面传输并影响板方程. 文献[1] 证明了在板方程上施加额外的控制器时, 该二维传输系统的能量呈指数衰减. 通过应用频域方法, 椭圆方程的正则 性理论等, 可以得到: 仅由热方程的耗散即可使得闭环系统指数稳定. 这一指数稳定的结论与相应的一维传输系统 的性质吻合. 最后, 文章还分析了不同传输边界条件下的板–热耦合系统的稳定性.     

一类偏泛函微分方程解的存在唯一性

研究了发展系统下一类偏泛函微分方程解的存在唯一性.假设该方程的线性部分生成一个Banach空间X上的一个解析半群,非线性部分是关于线性部分的分数幂Lipschitz连续.     

强连续线性算子半群在抛物型方程中的应用

给出了强连续线性算子半群在抛物型方程中的应用,得出了算子半群以-A为无穷小生成元的条件和抛物型方程混合问题（3）有唯一解的条件,并给出了相应证明．     

含中间幂等元的拟富足半群的构造

基于拓展的含中间幂等元的富足半群,给出了一类具有中间幂等元的拟富足半群的结构.为此研究了这一类具有中间冥等元的拟富足半群的构造方法.     

一类奇异半线性发展方程组解的Blow—up问题

讨论了一类具有奇异系数的发展方程组Cauchy问题的解在有限时间内的blow-up问题,并给出了相应的一些结果.     

具部分反射边界条件的多速非线性迁移方程的解

本文研究了一类具部分反射边界条件的非线性积分一微分方程组解的存在性及唯一性。     

Perturbation of strongly and polynomially stable Riesz-spectral operators

In this paper we consider bounded and relatively bounded finite rank perturbations of a Riesz-spectral operator generating a polynomially stable semigroup of linear operators on a Hilbert space. We concentrate on a commonly encountered situation where the spectrum of the unperturbed operator is contained in the open left half-plane of the complex plane and approaches the imaginary axis asymptotically. We present conditions on the perturbing operator such that the spectrum of the perturbed operator is contained in the open left half-plane of the complex plane and additional conditions for the strong and polynomial stabilities of the perturbed semigroup. We consider two applications of the perturbation results. In the first example we apply the results to the perturbation of a polynomially stabilized one-dimensional wave equation. In the second example we consider the perturbation of a closed-loop system consisting of a distributed parameter system and an observer-based feedback controller solving the robust output regulation problem related to an infinite-dimensional signal generator.