Global boundary stabilization to trajectories of the deterministic and stochastic porous-media equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/mcrf.2023037

Ionuţ Munteanu

引用次数: 0

Abstract

Here we deal with the problem of boundary asymptotic exponential stabilization of flows through porous media. More exactly we study the porous media equation with general monotone porosity in a bounded domain of dimension $ d = 1,2,3 $. We construct an explicit, linear, of finite-dimensional structure feedback controller with Dirichlet part-boundary actuation, which stabilizes any trajectory of the system, for any given initial data. The form of the controller is based on the spectrum of the Dirichlet-Laplace operator and ensures exponential decay to zero of the fluctuation variable for any a priori prescribed decay rate. Also, we extend these results to the case of porous media equation perturbed by Itô Lipschitz noise.

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确定性和随机多孔介质方程轨迹的全局边界稳定

本文研究多孔介质流动的边界渐近指数稳定问题。更确切地说，我们研究了一维$ d = 1,2,3 $的有界区域内具有一般单调孔隙率的多孔介质方程。我们构造了一个具有Dirichlet部分边界驱动的显式线性有限维结构反馈控制器，对于任何给定的初始数据，该控制器可以稳定系统的任何轨迹。控制器的形式是基于狄利克雷-拉普拉斯算子的频谱，并确保波动变量的指数衰减到零对于任何先验规定的衰减率。同时，我们将这些结果推广到受Itô Lipschitz噪声扰动的多孔介质方程。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.