Upper Semicontinuity of Random Attractors for Random Differential Equations with Nonlinear Diffusion Terms I: Finite-Dimensional Case

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-07-04 DOI:10.1007/s00245-024-10164-z

Anhui Gu

引用次数: 0

Abstract

The upper semicontinuity of random attractors for stochastic/random (partial) differential equations with nonlinear diffusion term is an unsolved problem. In this paper, we first show the existence of random attractor for the random differential equation with nonlinear diffusion term driven by the approximation of the fractional noise, and then prove the upper semicontinuity of the random attractors when the intensity of the approximations tends to zero. The obtained result partly gives an answer to this problem.

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带有非线性扩散项的随机微分方程的随机吸引子的上半连续性 I：有限维情况

带有非线性扩散项的随机/随机（偏）微分方程的随机吸引子的上半连续性是一个尚未解决的问题。在本文中，我们首先证明了由近似分式噪声驱动的带非线性扩散项的随机微分方程的随机吸引子的存在性，然后证明了当近似强度趋于零时随机吸引子的上半连续性。所得到的结果部分回答了这一问题。

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

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.