扩散松弛中出现的一种收敛模式

IF 0.6 4区数学 Q3 MATHEMATICS

Quarterly Journal of Mathematics Pub Date : 2024-02-20 DOI:10.1093/qmath/haae001

Nuno J Alves, João Paulos

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引用次数: 0

摘要

本文介绍了可测函数的收敛模式。给出了一个相关的考奇序列概念，并证明这一收敛概念在考奇序列收敛的意义上是完整的。此外，还研究了构成下的收敛性保持。这种收敛模式的起源在于证明欧拉系统的密度几乎无处不在（直到子序列）地向非线性扩散系统的密度收敛，这是松弛极限收敛的结果。

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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A mode of convergence arising in diffusive relaxation

In this work, a mode of convergence for measurable functions is introduced. A related notion of Cauchy sequence is given, and it is proved that this notion of convergence is complete in the sense that Cauchy sequences converge. Moreover, the preservation of convergence under composition is investigated. The origin of this mode of convergence lies in the path of proving that the density of a Euler system converges almost everywhere (up to subsequences) towards the density of a non-linear diffusion system, as a consequence of the convergence in the relaxation limit.

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来源期刊

Quarterly Journal of Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.