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
This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated byε-periodic holes of size ε. A Neumann condition is prescribe...This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated byε-periodic holes of size ε. A Neumann condition is prescribed on the boundary of the holes.The presence of the holes does not allow to prove a compactness of the solutions in L2. To overcome this difficulty, the authors introduce a suitable auxiliary linear problem to which a corrector result is applied. Then, the asymptotic behaviour of the semilinear problem as ε→ 0 is described, and the limit equation is given.展开更多
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
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Project supported by the European Research and Training Network "HMS 2000" of the European Union under Contract HPRN-2000-00109.
文摘This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated byε-periodic holes of size ε. A Neumann condition is prescribed on the boundary of the holes.The presence of the holes does not allow to prove a compactness of the solutions in L2. To overcome this difficulty, the authors introduce a suitable auxiliary linear problem to which a corrector result is applied. Then, the asymptotic behaviour of the semilinear problem as ε→ 0 is described, and the limit equation is given.
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).
