随机演化介质中卷积算子非自治演化问题的均匀化

IF 2.1 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI:10.1016/j.matpur.2025.103660

A. Piatnitski , E. Zhizhina

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引用次数: 0

摘要

研究了∂tu=L(t)u的非自治抛物方程的齐次化问题，该方程具有积分卷积型算子L(t)，该算子具有空间变量周期和时间平稳随机的非对称跳跃核。我们证明了解的时空演化渐近解耦，可以单独描述，并且在系数的附加混合条件下，均匀化方程是具有有限维乘性噪声的SPDE。

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Homogenization of non-autonomous evolution problems for convolution type operators in randomly evolving media

We study homogenization problem for non-autonomous parabolic equations of the form

\partial_{t} u = L (t) u

with an integral convolution type operator

L (t)

that has a non-symmetric jump kernel which is periodic in spatial variables and stationary random in time. We show that asymptotically the spatial and temporal evolutions of the solutions are getting decoupled and can be described separately, and, under additional mixing conditions on the coefficient, the homogenized equation is a SPDE with a finite dimensional multiplicative noise.

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来源期刊

Journal de Mathematiques Pures et Appliquees 数学-数学

CiteScore

4.30

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Published from 1836 by the leading French mathematicians, the Journal des Mathématiques Pures et Appliquées is the second oldest international mathematical journal in the world. It was founded by Joseph Liouville and published continuously by leading French Mathematicians - among the latest: Jean Leray, Jacques-Louis Lions, Paul Malliavin and presently Pierre-Louis Lions.