Volume 34, Issue 3
A Note on Homogenization of Parabolic Equation in Perforated Domains

Zhanying Yang, Wan Shu, Zhangping Pan & Chaoquan Peng

Commun. Math. Res., 34 (2018), pp. 230-240.

Published online: 2019-12

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  • Abstract

We are concerned with a class of parabolic equations in periodically perforated domains with a homogeneous Neumann condition on the boundary of holes. By using the periodic unfolding method in perforated domains, we obtain the homogenization results under the conditions slightly weaker than those in the corresponding case considered by Nandakumaran and Rajesh (Nandakumaran A K, Rajesh M. Homogenization of a parabolic equation in perforated domain with Neumann boundary condition. Proc. Indian Acad. Sci. (Math. Sci.), 2002, 112(1): 195–207). Moreover, these results generalize those obtained by Donato and Nabil (Donato P, Nabil A. Homogenization and correctors for the heat equation in perforated domains. Ricerche di Matematica L. 2001, 50: 115–144).

  • Keywords

parabolic equation, perforated domain, homogenization, periodic unfolding method

  • AMS Subject Headings

35B27, 35K55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yangzhanying8011@163.com (Zhanying Yang)

  • BibTex
  • RIS
  • TXT
@Article{CMR-34-230, author = {Yang , Zhanying and Shu , Wan and Pan , Zhangping and Peng , Chaoquan}, title = {A Note on Homogenization of Parabolic Equation in Perforated Domains}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {34}, number = {3}, pages = {230--240}, abstract = {

We are concerned with a class of parabolic equations in periodically perforated domains with a homogeneous Neumann condition on the boundary of holes. By using the periodic unfolding method in perforated domains, we obtain the homogenization results under the conditions slightly weaker than those in the corresponding case considered by Nandakumaran and Rajesh (Nandakumaran A K, Rajesh M. Homogenization of a parabolic equation in perforated domain with Neumann boundary condition. Proc. Indian Acad. Sci. (Math. Sci.), 2002, 112(1): 195–207). Moreover, these results generalize those obtained by Donato and Nabil (Donato P, Nabil A. Homogenization and correctors for the heat equation in perforated domains. Ricerche di Matematica L. 2001, 50: 115–144).

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.03.05}, url = {http://global-sci.org/intro/article_detail/cmr/13488.html} }
TY - JOUR T1 - A Note on Homogenization of Parabolic Equation in Perforated Domains AU - Yang , Zhanying AU - Shu , Wan AU - Pan , Zhangping AU - Peng , Chaoquan JO - Communications in Mathematical Research VL - 3 SP - 230 EP - 240 PY - 2019 DA - 2019/12 SN - 34 DO - http://doi.org/10.13447/j.1674-5647.2018.03.05 UR - https://global-sci.org/intro/article_detail/cmr/13488.html KW - parabolic equation, perforated domain, homogenization, periodic unfolding method AB -

We are concerned with a class of parabolic equations in periodically perforated domains with a homogeneous Neumann condition on the boundary of holes. By using the periodic unfolding method in perforated domains, we obtain the homogenization results under the conditions slightly weaker than those in the corresponding case considered by Nandakumaran and Rajesh (Nandakumaran A K, Rajesh M. Homogenization of a parabolic equation in perforated domain with Neumann boundary condition. Proc. Indian Acad. Sci. (Math. Sci.), 2002, 112(1): 195–207). Moreover, these results generalize those obtained by Donato and Nabil (Donato P, Nabil A. Homogenization and correctors for the heat equation in perforated domains. Ricerche di Matematica L. 2001, 50: 115–144).

Zhanying Yang, Wan Shu, Zhangping Pan & Chaoquan Peng. (2019). A Note on Homogenization of Parabolic Equation in Perforated Domains. Communications in Mathematical Research . 34 (3). 230-240. doi:10.13447/j.1674-5647.2018.03.05
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