Multiscale convergence and reiterated homogenization of parabolic problems

Holmbom, Anders, Svanstedt, Nils, and Wellander, Niklas. "Multiscale convergence and reiterated homogenization of parabolic problems." Applications of Mathematics 50.2 (2005): 131-151. <http://eudml.org/doc/33212>.

@article{Holmbom2005,
abstract = {Reiterated homogenization is studied for divergence structure parabolic problems of the form $\partial u_\{\varepsilon \}/\partial t - \operatorname\{div\}\bigl (a\bigl (x,x/\varepsilon ,x/\varepsilon ^2, t,t/\varepsilon ^\{k\}\bigr )\nabla u_\{\varepsilon \}\bigr )=f$. It is shown that under standard assumptions on the function $a(x,y_1,y_2,t,\tau )$ the sequence $\lbrace u_\epsilon \rbrace $ of solutions converges weakly in $L^2(0,T;H^1_0(\Omega ))$ to the solution $u$ of the homogenized problem $\partial u/\partial t -\operatorname\{div\}(b(x,t)\nabla u)=f$.},
author = {Holmbom, Anders, Svanstedt, Nils, Wellander, Niklas},
journal = {Applications of Mathematics},
keywords = {reiterated homogenization; multiscale convergence; parabolic equation; reiterated homogenization; multiscale convergence; parabolic equation},
language = {eng},
number = {2},
pages = {131-151},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Multiscale convergence and reiterated homogenization of parabolic problems},
url = {http://eudml.org/doc/33212},
volume = {50},
year = {2005},
}

TY - JOUR
AU - Holmbom, Anders
AU - Svanstedt, Nils
AU - Wellander, Niklas
TI - Multiscale convergence and reiterated homogenization of parabolic problems
JO - Applications of Mathematics
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 2
SP - 131
EP - 151
AB - Reiterated homogenization is studied for divergence structure parabolic problems of the form $\partial u_{\varepsilon }/\partial t - \operatorname{div}\bigl (a\bigl (x,x/\varepsilon ,x/\varepsilon ^2, t,t/\varepsilon ^{k}\bigr )\nabla u_{\varepsilon }\bigr )=f$. It is shown that under standard assumptions on the function $a(x,y_1,y_2,t,\tau )$ the sequence $\lbrace u_\epsilon \rbrace $ of solutions converges weakly in $L^2(0,T;H^1_0(\Omega ))$ to the solution $u$ of the homogenized problem $\partial u/\partial t -\operatorname{div}(b(x,t)\nabla u)=f$.
LA - eng
KW - reiterated homogenization; multiscale convergence; parabolic equation; reiterated homogenization; multiscale convergence; parabolic equation
UR - http://eudml.org/doc/33212
ER -