随机非自治抛物线算子的高阶均质化

IF 1.4 3区数学 Q2 MATHEMATICS, APPLIED Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-02-13 DOI:10.1007/s40072-023-00323-8

Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier

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引用次数: 0

摘要

我们考虑的是具有快速振荡系数的发散形式二阶抛物线算子的考奇问题，该系数在空间变量上是周期性的，在时间上是随机静态遍历的。正如 Zhikov 等人（Mat Obshch 45:182-236, 1982）和 Kleptsyna 和 Piatnitski（Homogenization and applications to material sciences.GAKUTO Internat Ser Math Sci Appl vol 9, pp 241-255.Gakkōtosho, Tokyo, 1995）在这种情况下均质化算子是确定性的。本文的重点是非扩散缩放情况下解的扩散近似，即空间变量的振荡快于时间变量的振荡。我们的目标是研究原始问题和同质化问题的解之间的归一化差异的渐近行为。

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Higher order homogenization for random non-autonomous parabolic operators

We consider Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variables and random stationary ergodic in time. As was proved in Zhikov et al. (Mat Obshch 45:182–236, 1982) and Kleptsyna and Piatnitski (Homogenization and applications to material sciences. GAKUTO Internat Ser Math Sci Appl vol 9, pp 241–255. Gakkōtosho, Tokyo, 1995) in this case the homogenized operator is deterministic. The paper focuses on the diffusion approximation of solutions in the case of non-diffusive scaling, when the oscillation in spatial variables is faster than that in temporal variable. Our goal is to study the asymptotic behaviour of the normalized difference between solutions of the original and the homogenized problems.

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来源期刊

Stochastics and Partial Differential Equations-Analysis and Computations Mathematics-Modeling and Simulation

CiteScore

2.70

自引率

13.30%

发文量

期刊介绍： Stochastics and Partial Differential Equations: Analysis and Computations publishes the highest quality articles presenting significantly new and important developments in the SPDE theory and applications. SPDE is an active interdisciplinary area at the crossroads of stochastic anaylsis, partial differential equations and scientific computing. Statistical physics, fluid dynamics, financial modeling, nonlinear filtering, super-processes, continuum physics and, recently, uncertainty quantification are important contributors to and major users of the theory and practice of SPDEs. The journal is promoting synergetic activities between the SPDE theory, applications, and related large scale computations. The journal also welcomes high quality articles in fields strongly connected to SPDE such as stochastic differential equations in infinite-dimensional state spaces or probabilistic approaches to solving deterministic PDEs.