Nonlinear partial differential equations on noncommutative Euclidean spaces

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-02-26 DOI:10.1007/s00028-023-00928-5

引用次数: 0

Abstract

Noncommutative Euclidean spaces—otherwise known as Moyal spaces or quantum Euclidean spaces—are a standard example of a non-compact noncommutative geometry. Recent progress in the harmonic analysis of these spaces gives us the opportunity to highlight some of their peculiar features. For example, the theory of nonlinear partial differential equations has unexpected properties in this noncommutative setting. We develop elementary aspects of paradifferential calculus for noncommutative Euclidean spaces and give some applications to nonlinear evolution equations. We demonstrate how the analysis of some equations radically simplifies in the strictly noncommutative setting.

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非交换欧几里得空间上的非线性偏微分方程

摘要非交换欧几里得空间--又称莫亚尔空间或量子欧几里得空间--是非紧凑非交换几何的一个标准例子。对这些空间进行调和分析的最新进展使我们有机会强调它们的一些特殊性。例如，非线性偏微分方程理论在这种非交换环境中具有意想不到的特性。我们发展了非交换欧几里得空间的范差分微积分的基本方面，并给出了非线性演化方程的一些应用。我们展示了某些方程的分析是如何在严格的非交换环境中从根本上简化的。

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

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators