Chinese Quarterly Journal of Mathematics ›› 2024, Vol. 39 ›› Issue (2): 171-179.doi: 10.13371/j.cnki.chin.q.j.m.2024.02.005

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Strong Convergence Rates of Reiterated Homogenization Problems

ZHAO Jie, WU Xi-min, WANG Juan   

  1. (College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China)
  • Received:2023-03-06 Online:2024-06-30 Published:2024-06-30
  • Contact: ZHAO Jie (1983-), male, native of Kaifeng, Henan, associate professor of Zhongyuan University of Technology, engages in partial differential equations; E-mail: kaifengajie@163.com
  • About author: 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.
  • 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).

Abstract:  In this paper, we study the reiterated homogenization operators Lε =−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 H0and Lconvergence estimates of solutions.

Key words: Convergence theorems, Weak solutions, Homogenization operators

CLC Number: