论文标题
无限维线性系统的阳性
Positivity of infinite-dimensional linear systems
论文作者
论文摘要
在本文中，我们研究了具有无界输入和输出运算符的无限维线性系统的适合性和积极性。特别是，我们表征了这类系统的内部和外部积极性。后者的努力部分是通过对良好的积极对照/观察系统的完整描述进行的。积极良好的线性系统的一个有趣特征是，从salamon和weiss的意义上讲，弱的规律性和强大的规律性是等效的。此外，我们为阳性半群的零级可接受性提供了足够的条件。在阳性半群的积极扰动的背景下，我们建立了两个扰动结果，即Desch-Schappacher扰动和Staffans-Weiss扰动。至于说明，这些发现用于研究有限网络上具有非本地边界条件的线性玻尔兹曼方程的正聚溶液的存在和独特性。
In this paper, we investigate the well-posedness and positivity property of infinite-dimensional linear system with unbounded input and output operators. In particular, we characterize the internal and external positivity for this class of systems. This latter effort is motivated in part by a complete description of well-posed positive control/observation systems. An interesting feature of positive well-posed linear systems is that weak regularity and strong regularity, in the sense of Salamon and Weiss, are equivalent. Moreover, we provide sufficient conditions for zero-class admissibility for positive semigroups. In the context of positive perturbations of positive semigroups, we establish two perturbation results, namely the Desch-Schappacher perturbation and the Staffans-Weiss perturbation. As for illustration, these findings are applied to investigate the existence and uniqueness of a positive mild solution of the linear Boltzmann equation with non-local boundary conditions on finite network.
