We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization ...We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization and corrector results which generalize those by Donato and Nabil(2001).展开更多
Making use of the periodic unfolding method,the authors give an elementary proof for the periodic homogenization of the elastic torsion problem of an infinite 3dimensional rod with a multiply-connected cross section a...Making use of the periodic unfolding method,the authors give an elementary proof for the periodic homogenization of the elastic torsion problem of an infinite 3dimensional rod with a multiply-connected cross section as well as for the general electroconductivity problem in the presence of many perfect conductors(arising in resistivity well-logging).Both problems fall into the general setting of equi-valued surfaces with corresponding assigned total fluxes.The unfolding method also gives a general corrector result for these problems.展开更多
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 ob...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）.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11401595)
文摘We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization and corrector results which generalize those by Donato and Nabil(2001).
基金Supported by the National Natural Science Foundation of China (No. 11121101)the National Basic Research Program of China (No. 2013CB834100)
文摘Making use of the periodic unfolding method,the authors give an elementary proof for the periodic homogenization of the elastic torsion problem of an infinite 3dimensional rod with a multiply-connected cross section as well as for the general electroconductivity problem in the presence of many perfect conductors(arising in resistivity well-logging).Both problems fall into the general setting of equi-valued surfaces with corresponding assigned total fluxes.The unfolding method also gives a general corrector result for these problems.
基金The NSF(11401595)of Chinathe Nationalities Innovation Foundation(2018sycxjj113)of South-central University for Postgraduate
文摘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）.
