Homogenization of parabolic equations an alternative approach and some corrector-type results

 Access to full text

 Full (PDF)

1. Sobolev Spaces. Academic Press, New York, 1975. (1975) MR0450957
2. Two-scale convergence and homogenization of periodic structures, School on homogenization, ICTP, Trieste, September 6–17, 1993. (1993) 
3. Homogenization of the unsteady Stokes equation in porous media, Progress in pdes: calculus of variation, applications, Pitman Research notes in mathematics Series 267, C. Bandle et al. (eds.), Longman Higher Education, New York, 1992. (1992) MR1194192
4. 10.1137/0523084, SIAM Journal of Mathematical Analysis, 23 (1992), no. 6, 1482–1518. (1992) Zbl0770.35005MR1185639DOI10.1137/0523084
5. Lineare Funktionalanalysis, Springer-Verlag, 1985. (1985) Zbl0577.46001
6. Variational Convergence of Functions and Operators, Pitman Publishing Limited, 1984. (1984) MR0773850
7. Asymptotic Analysis for Periodic Structures, Studies in Mathematics and its Applications, North-Holland, 1978. (1978) MR0503330
8. Interpolation Spaces. An Introduction, Grundlehren der mathematischen Wissenschaft, Springer-Verlag, 1976. (1976) MR0482275
9. Correctors for the homogenization of the wave and heat equation, J. Math. Pures Appl 9 (1992). (1992) MR1172450
10. Navier-Stokes equations, The University of Chicago Press, Chicago, 1989. (1989) MR0972259
11. An introduction to $\Gamma$-convergence. Progress in Nonlinear Differential Equations and their Applications, Volume 8, Birkhäuser Boston, 1993. (1993) MR1201152
12. An introduction to homogenization and G-convergence, School on homogenization, ICTP, Trieste, September 6–17, 1993. (1993) 
13. Functional Analysis, Holt, Rinehart and Winston, New York, 1965. (1965) Zbl0182.16101MR0221256
14. Some results for periodic and non-periodic two-scale convergence, Working paper No. 33 University of Gävle/Sandviken, 1996. (1996) 
15. Function Spaces, Nordhoff International, Leyden, 1977. (1977) Zbl0364.46022MR0541734
16. Non Homogeneous Boundary Value problems and Applications II, Springer-Verlag, Berlin, 1972. (1972) 
17. Steady and evolution Stokes equations in a porous media with Non-homogeneous boundary data. A homogenization process, Differential and Integral Equations 5 (1992), no. 1, 73–93. (1992) MR1141728
18. 10.1137/0520043, SIAM Journal of Mathematical Analysis 20 (1989), no. 3, 608–623. (1989) Zbl0688.35007MR0990867DOI10.1137/0520043
19. Thèse d’Etat, Université Paris 6, 1984. (1984) 
20. The Homogenization Method—An Introduction, Studentlitteratur Publishing, 1993. (1993) MR1250833
21. Non-Homogeneous Media and Vibration Theory, Springer Verlag, 1980. (1980) Zbl0432.70002
22. Navier Stokes Equation, North-Holland, 1984. (1984) MR0769654
23. Nonlinear Functional Analysis and its Applications II, Springer Verlag, 1990. (1990) Zbl0684.47029MR0816732
24. Weakly Differentiable Functions, Springer Verlag, 1989. (1989) Zbl0692.46022MR1014685

1. Hongwei Lou, Optimality conditions for semilinear parabolic equations with controls in leading term
2. Hongwei Lou, Optimality conditions for semilinear parabolic equations with controls in leading term
3. Niklas Wellander, Homogenization of the Maxwell equations: Case I. Linear theory
4. Anders Holmbom, Nils Svanstedt, Niklas Wellander, Multiscale convergence and reiterated homogenization of parabolic problems
5. Luděk Nechvátal, Worst scenario method in homogenization. Linear case
6. Pernilla Johnsen, Tatiana Lobkova, Homogenization of a linear parabolic problem with a certain type of matching between the microscopic scales
7. Liselott Flodén, Marianne Olsson, Homogenization of some parabolic operators with several time scales
8. Tatiana Danielsson, Pernilla Johnsen, Homogenization of linear parabolic equations with three spatial and three temporal scales for certain matchings between the microscopic scales
9. Luděk Nechvátal, Alternative approaches to the two-scale convergence
10. Jiří Vala, The method of Rothe and two-scale convergence in nonlinear problems