随机演化方程的临界变分设置

IF 1.5 1区 数学 Q2 STATISTICS & PROBABILITY
Antonio Agresti, Mark Veraar
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引用次数: 0

摘要

在本文中,我们介绍了准线性或半线性抛物线随机演化方程的临界变分设置。我们的结果改进了经典变分设置中的许多抽象结果。特别是,我们能够用更灵活的局部 Lipschitz 条件取代通常的弱单调性或局部单调性条件。此外,乘法噪声的通常增长条件也被大大削弱。我们的新设定提供了局部和全局存在性和唯一性成立的一般条件。此外,我们还证明了对初始数据的连续依赖性。我们证明,许多经典变分设置无法涵盖的经典 SPDEs,确实适合临界变分设置。尤其是 Cahn-Hilliard 方程、驯服 Navier-Stokes 方程和 Allen-Cahn 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。
The critical variational setting for stochastic evolution equations

In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz condition. Moreover, the usual growth conditions on the multiplicative noise are weakened considerably. Our new setting provides general conditions under which local and global existence and uniqueness hold. In addition, we prove continuous dependence on the initial data. We show that many classical SPDEs, which could not be covered by the classical variational setting, do fit in the critical variational setting. In particular, this is the case for the Cahn–Hilliard equation, tamed Navier–Stokes equations, and Allen–Cahn equation.

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来源期刊
Probability Theory and Related Fields
Probability Theory and Related Fields 数学-统计学与概率论
CiteScore
3.70
自引率
5.00%
发文量
71
审稿时长
6-12 weeks
期刊介绍: Probability Theory and Related Fields publishes research papers in modern probability theory and its various fields of application. Thus, subjects of interest include: mathematical statistical physics, mathematical statistics, mathematical biology, theoretical computer science, and applications of probability theory to other areas of mathematics such as combinatorics, analysis, ergodic theory and geometry. Survey papers on emerging areas of importance may be considered for publication. The main languages of publication are English, French and German.
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