Geodesic
Homogenization of parabolic equations an alternative approach and some corrector-type results
Applications of Mathematics, Tome 42 (1997) no. 5, pp. 321-343 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We extend and complete some quite recent results by Nguetseng [Ngu1] and Allaire [All3] concerning two-scale convergence. In particular, a compactness result for a certain class of parameterdependent functions is proved and applied to perform an alternative homogenization procedure for linear parabolic equations with coefficients oscillating in both their space and time variables. For different speeds of oscillation in the time variable, this results in three cases. Further, we prove some corrector-type results and benefit from some interpolation properties of Sobolev spaces to identify regularity assumptions strong enough for such results to hold.
We extend and complete some quite recent results by Nguetseng [Ngu1] and Allaire [All3] concerning two-scale convergence. In particular, a compactness result for a certain class of parameterdependent functions is proved and applied to perform an alternative homogenization procedure for linear parabolic equations with coefficients oscillating in both their space and time variables. For different speeds of oscillation in the time variable, this results in three cases. Further, we prove some corrector-type results and benefit from some interpolation properties of Sobolev spaces to identify regularity assumptions strong enough for such results to hold.
DOI : 10.1023/A:1023049608047
Classification : 35B27, 35K20, 35K99, 73B27, 73K20, 74E05, 74E30
Keywords: partial differential equations; homogenization; two-scale convergence; linear parabolic equations; oscillating coefficients in space and time variable; dissimilar speeds of oscillation; admissible test functions; corrector results; compactness result; interpolation; coefficients oscillating in space and time 
@article{10_1023_A:1023049608047,
     author = {Holmbom, Anders},
     title = {Homogenization of parabolic equations an alternative approach and some corrector-type results},
     journal = {Applications of Mathematics},
     pages = {321--343},
     year = {1997},
     volume = {42},
     number = {5},
     doi = {10.1023/A:1023049608047},
     mrnumber = {1467553},
     zbl = {0898.35008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1023/A:1023049608047/}
}
TY  - JOUR
AU  - Holmbom, Anders
TI  - Homogenization of parabolic equations an alternative approach and some corrector-type results
JO  - Applications of Mathematics
PY  - 1997
SP  - 321
EP  - 343
VL  - 42
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.1023/A:1023049608047/
DO  - 10.1023/A:1023049608047
LA  - en
ID  - 10_1023_A:1023049608047
ER  - 
%0 Journal Article
%A Holmbom, Anders
%T Homogenization of parabolic equations an alternative approach and some corrector-type results
%J Applications of Mathematics
%D 1997
%P 321-343
%V 42
%N 5
%U http://geodesic.mathdoc.fr/articles/10.1023/A:1023049608047/
%R 10.1023/A:1023049608047
%G en
%F 10_1023_A:1023049608047
Holmbom, Anders. Homogenization of parabolic equations an alternative approach and some corrector-type results. Applications of Mathematics, Tome 42 (1997) no. 5, pp. 321-343. doi: 10.1023/A:1023049608047

Cité par Sources :