一类超强退化抛物算子的Carleman不等式及其应用

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-04-20 DOI:10.14232/ejqtde.2023.1.9

Equations Bruno S. V. Ara'ujo, R. Demarque, L. Viana

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引用次数: 0

摘要

本文给出了一类超强退化抛物型线性问题伴随方程的一个新的Carleman估计。我们的方法在控制域上考虑了一个标准的几何强加，它通常不能被去除。此外，我们还应用上述主要不等式来研究两个非线性抛物型系统的零可控性。第一个应用是关于一些依赖不动点参数的半线性方程的全局零可控性结果。在第二部分中，利用反函数定理，也得到了一些非局部项方程的局部零可控性。

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Carleman inequality for a class of super strong degenerate parabolic operators and applications

In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can not be removed in general. Additionally, we also apply the aforementioned main inequality in order to investigate the null controllability of two nonlinear parabolic systems. The first application is concerned a global null controllability result obtained for some semilinear equations, relying on a fixed point argument. In the second one, a local null controllability for some equations with nonlocal terms is also achieved, by using an inverse function theorem.

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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.