Well-posedness and stability of a class of linear systems

IF 0.8 3区 数学 Q2 MATHEMATICS
Yassine El Gantouh
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引用次数: 0

Abstract

The aim of this work is to provide useful criteria for well-posedness, positivity and stability of a class of infinite-dimensional linear systems. These criteria are based on an inverse estimate with respect to the Hille–Yosida Theorem. Indeed, we establish a generation result for perturbed positive operator semigroups, namely, for positive unbounded boundary perturbations. This unifies previous results available in the literature and that were established separately so far. We also prove that uniform exponential stability persists under unbounded boundary perturbations. Finally, applications to a Boltzmann equation with non-local boundary conditions on a finite network and a size-dependent population system with delayed birth process are also presented.

一类线性系统的良好性和稳定性
这项工作的目的是为一类无穷维线性系统的拟合性、实在性和稳定性提供有用的标准。这些标准基于希勒-约西达定理的逆估计。事实上,我们为扰动正算子半群建立了一个生成结果,即针对正的无边界扰动。这统一了以往文献中单独建立的结果。我们还证明了无界边界扰动下的均匀指数稳定性。最后,我们还介绍了有限网络上具有非局部边界条件的玻尔兹曼方程和具有延迟出生过程的规模依赖型人口系统的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Positivity
Positivity 数学-数学
CiteScore
1.80
自引率
10.00%
发文量
88
审稿时长
>12 weeks
期刊介绍: The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.
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