Indexed by: Journal paper

First Author: Junlong Chen

Correspondence Author: Yanbin Tang

Journal: Networks and Heterogeneous Media

Included Journals: SCI

Affiliation of Author(s): Huazhong University of Science and Technology

Place of Publication: USA

Discipline: Science

First-Level Discipline: Mathematics

Funded by: 国家自然科学基金

Document Type: J

Volume: 18

Issue: 3

Page Number: 1118-1177

ISSN No.: 1556-1801

DOI number: 10.3934/nhm.2023049

Date of Publication: 2023-04-03

Impact Factor: 1.41

Abstract: 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.

Number of Words: 60000

Links to published journals: http://aimspress.com/article/doi/10.3934/nhm.2023049