Geodesic
Multiscale convergence and reiterated homogenization of parabolic problems
Applications of Mathematics, Tome 50 (2005) no. 2, pp. 131-151

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Reiterated homogenization is studied for divergence structure parabolic problems of the form $\partial u_{\varepsilon }/\partial t - \div \bigl (a\bigl (x,x/\varepsilon ,x/\varepsilon ^2, t,t/\varepsilon ^{k}\bigr )\nabla u_{\varepsilon }\bigr )=f$. 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 $\partial u/\partial t -\div (b(x,t)\nabla u)=f$.
DOI : 10.1007/s10492-005-0009-z
Classification : 35B27, 35K20
Keywords: reiterated homogenization; multiscale convergence; parabolic equation 
@article{10_1007_s10492_005_0009_z,
     author = {Holmbom, Anders and Svanstedt, Nils and Wellander, Niklas},
     title = {Multiscale convergence and reiterated homogenization of parabolic problems},
     journal = {Applications of Mathematics},
     pages = {131--151},
     publisher = {mathdoc},
     volume = {50},
     number = {2},
     year = {2005},
     doi = {10.1007/s10492-005-0009-z},
     mrnumber = {2125155},
     zbl = {1099.35011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-005-0009-z/}
}
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
SP  - 131
EP  - 151
VL  - 50
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-005-0009-z/
DO  - 10.1007/s10492-005-0009-z
LA  - en
ID  - 10_1007_s10492_005_0009_z
ER  - 
%0 Journal Article
%A Holmbom, Anders
%A Svanstedt, Nils
%A Wellander, Niklas
%T Multiscale convergence and reiterated homogenization of parabolic problems
%J Applications of Mathematics
%D 2005
%P 131-151
%V 50
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-005-0009-z/
%R 10.1007/s10492-005-0009-z
%G en
%F 10_1007_s10492_005_0009_z
Holmbom, Anders; Svanstedt, Nils; Wellander, Niklas. Multiscale convergence and reiterated homogenization of parabolic problems. Applications of Mathematics, Tome 50 (2005) no. 2, pp. 131-151. doi: 10.1007/s10492-005-0009-z

Cité par Sources :