Strong Convergence Rates of Reiterated Homogenization Problems

ZHAO Jie, WU Xi-min, WANG Juan

doi:10.13371/j.cnki.chin.q.j.m.2024.02.005

Chinese Quarterly Journal of Mathematics >

2024 , Vol. 39 >Issue 2: 171 - 179

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.02.005

Strong Convergence Rates of Reiterated Homogenization Problems

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(College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China)

ZHAO Jie (1983-), male, native of Kaifeng, Henan, associate professor of Zhongyuan University of Technology, engages in partial differential equations; WU Xi-min (1997-), male, native of Fuzhou, Jiangxi, graduate student of Zhongyuan University of Technology, engages in partial differential equations; WANG Juan (1984-), female, native of Kaifeng, Henan, lecturer of Zhongyuan University of Technology, engages in partial differential equations.

Received date: 2023-03-06

Online published: 2024-06-30

Supported by

Supported by National Natural Science Foundation of China (Grant Nos. 11861045, 11626239 and 11701449); China Scholarship Council (Grant No. 201708410483); Education Department of Henan Province (Grant No. 18A110037).

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Abstract

In this paper, we study the reiterated homogenization operators L_ε=−div(A(x/ε,x/ε2)∇). We establish the homogenized problem and representation equation by introducing the two correctors. As a consequence, we obtain the H₀¹and L²convergence estimates of solutions.

Key words： Convergence theorems; Weak solutions; Homogenization operators

Cite this article

ZHAO Jie, WU Xi-min, WANG Juan . Strong Convergence Rates of Reiterated Homogenization Problems[J]. Chinese Quarterly Journal of Mathematics, 2024 , 39(2) : 171 -179 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.005

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