论文类型：期刊论文

第一作者：Junlong Chen

通讯作者：Yanbin Tang

发表刊物：Networks and Heterogeneous Media

收录刊物：SCI

所属单位：华中科技大学

刊物所在地：USA

学科门类：理学

一级学科：数学

项目来源：国家自然科学基金

文献类型：J

卷号：18

期号：3

页面范围：1118-1177

ISSN号：1556-1801

DOI码：10.3934/nhm.2023049

发表时间：2023-04-03

影响因子：1.41

摘要：This paper is devoted to the homogenization of a class of nonlinear nonlocal parabolic equations with time dependent coefficients in a periodic and stationary structure. In the first part, we consider the homogenization problem with a periodic structure. Inspired by the idea of Akagi and Oka for local nonlinear homogenization, by a change of unknown function, we transform the nonlinear nonlocal term in space into a linear nonlocal scaled diffusive term, while the corresponding linear time derivative term becomes a nonlinear one. By constructing some corrector functions, for different time scales r and the nonlinear parameter p, we obtain that the limit equation is a local nonlinear diffusion equation with coefficients depending on r and p. In addition, we also consider the homogenization of the nonlocal porous medium equation with non negative initial values and get similar homogenization results. In the second part, we consider the previous problem in a stationary environment and get some similar homogenization results. The novelty of this paper is two folds. First, for the determination equation with a periodic structure, our study complements the results in literature for r = 2 and p = 1. Second, we consider the corresponding equation with a stationary structure.

字数：60000

发布期刊链接：http://aimspress.com/article/doi/10.3934/nhm.2023049