TY - JOUR
T1 - Two-parameter homogenization for a nonlinear periodic Robin problem for the Poisson equation
T2 - a functional analytic approach
AU - Lanza de Cristoforis, Massimo
AU - Musolino, Paolo
PY - 2018/1/1
Y1 - 2018/1/1
N2 - We consider a nonlinear Robin problem for the Poisson equation in an unbounded periodically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter δδ . The relative size of each periodic perforation is instead determined by a positive parameter ϵϵ . We prove the existence of a family of solutions which depends on ϵϵ and δδ and we analyze the behavior of such a family as (ϵ,δ)(ϵ,δ) tends to (0, 0) by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory.
AB - We consider a nonlinear Robin problem for the Poisson equation in an unbounded periodically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter δδ . The relative size of each periodic perforation is instead determined by a positive parameter ϵϵ . We prove the existence of a family of solutions which depends on ϵϵ and δδ and we analyze the behavior of such a family as (ϵ,δ)(ϵ,δ) tends to (0, 0) by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory.
KW - nonlinear robin problem
KW - singularly perturbed domain
KW - poisson equation
KW - periodically perforated domain
KW - homogenization
KW - real analytic continuation in Banach space
U2 - 10.1007/s13163-017-0242-5
DO - 10.1007/s13163-017-0242-5
M3 - Article
SN - 1139-1138
VL - 31
SP - 63
EP - 110
JO - Revista Matemática Complutense
JF - Revista Matemática Complutense
IS - 1
ER -