内集退化Schrödinger方程的可控性

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2024-12-20 DOI:10.1002/mana.202300252

Mohamed Alahyane, Abderrazak Chrifi, Younes Echarroudi

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引用次数: 0

摘要

本文研究了一类线性退化Schrödinger方程的零可控性，该方程的退化发生在（0,1）的内部子集上，即：∃w1∧(0,1)，使得∀x∈w1， k (x) = 0 $(0,1), \text{ that is, } \exists W_{1}\subset \subset (0,1), \text{ such that } \forall x\in W_{1}, \text{ } k(x)=0$，k $k$代表量子扩散。更准确地说，我们使用建立在一个新的Carleman估计和一个新的可观测性不等式基础上的经典过程来关注零可控性现象。

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On the controllability of an interior set degenerate Schrödinger equation

In this paper, we are interested on the null controllability property of a linear degenerate Schrödinger equation with a degeneracy occurring on an interior subset of $(0, 1), that is, \exists W_{1} \subset \subset (0, 1), such that \forall x \in W_{1}, k (x) = 0$ , where $k$ stands for the quantum diffusion. More precisely, we are concerned with the null controllability phenomenon using the classical procedure founded on a new Carleman estimate and afterward a newfangled observability inequality.

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index