Open Access
| Issue |
ESAIM: COCV
Volume 32, 2026
|
|
|---|---|---|
| Article Number | 26 | |
| Number of page(s) | 20 | |
| DOI | https://doi.org/10.1051/cocv/2026006 | |
| Published online | 03 April 2026 | |
- R.J. DiPerna and P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 (1989) 511–547. [Google Scholar]
- Y. Brenier, Remarks on some linear hyperbolic equations with oscillatory coefficients. Proceedings of the Third International Conference on Hyperbolic Problems (Uppsala 1990), vol. I, II. Studentlitteratur, Lund (1991) 119–130. [Google Scholar]
- G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608–623. [Google Scholar]
- G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992) 1482–1518. [Google Scholar]
- T.Y. Hou and X. Xin, Homogenization of linear transport equations with oscillatory vector fields. SIAM J. Appl. Math. 52 (1992) 34–45. [Google Scholar]
- F. Golse, Moyennisation des champs de vecteurs et EDP. Journées Équations aux Dérivées Partielles [The averaging of vector fields and PDEs], Saint Jean de Monts 1990, Exp. no. XVI. Ecole Polytech. Palaiseau (1990) 17 (in French). [Google Scholar]
- F. Golse, Perturbations de systèmes dynamiques et moyennisation en vitesse des EDP [On perturbations of dynamical systems and the velocity averaging method for PDEs]. C. R. Acad. Sci. Paris Ser. I Math. 314 (1992) 115–120 (in French). [Google Scholar]
- T. Tassa, Homogenization of two-dimensional linear flows with integral invariance. SIAM J. Appl. Math. 57 (1997) 1390–1405. [Google Scholar]
- R. Peirone, Convergence of solutions of linear transport equations. Ergodic Theory Dynam. Syst. 23 (2003) 919–933. [Google Scholar]
- R. Peirone, Homogenization of ODE's in ℝN. Ann. Mat. Pura Appl. 198 (2019) 869–879. [Google Scholar]
- M. Briane and L. Hervé, A picture of the ODE's flow in the torus: from anywhere or almost-anywhere asymptotics to homogenization of transport equations. J. Differ. Equ. 304 (2021) 165–190. [Google Scholar]
- L. Tartar, Nonlocal effects induced by homogenization. Partial Differential Equations and the Calculus of Variations, Vol. II, edited by F. Colombini, et al. Progr. Nonlinear Differential Equations Appl. 2. Birkh'auser Boston, Boston, MA (1989) 925–938. [Google Scholar]
- M.L. Mascarenhas, A linear homogenization problem with time dependent coefficient. Trans. Am. Math. Soc. 281 (1984) 179–195. [Google Scholar]
- Y. Amirat, K. Hamdache and A. Ziani, Homogénéisation d'équations hyperboliques du premier ordre et application aux écoulements miscibles en milieu poreux [Homogenization of a system of first-order hyperbolic equations and application to miscible flows in a porous medium]. Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989) 397–417 (in French). [Google Scholar]
- Y. Amirat, K. Hamdache and A. Ziani, Some results on homogenization of convection-diffusion equations. Arch. Rational Mech. Anal. 114 (1991) 155–178. [Google Scholar]
- Y. Amirat, K. Hamdache and A. Ziani, Homogenisation of parametrised families of hyperbolic problems. Proc. Roy. Soc. Edinburgh Sect. A 120 (1992) 199–221. [Google Scholar]
- M. Briane, G.W. Milton and A. Treibergs, Which electric fields are realizable in conducting materials? ESAIM: Math. Model. Numer. Anal. 48 (2014) 307–323. [Google Scholar]
- I.P. Cornfeld, S.V. Fomin and Ya.G. Sinaĭ, Ergodic Theory, translated from the Russian by A.B. Sosinskii, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] vol. 245. Springer-Verlag, New York (1982) 486. [Google Scholar]
- E. Weinan, Homogenization of linear and nonlinear transport equations. Commun. Pure Appl. Math. 45 (1992) 301–326. [Google Scholar]
- M.R. Herman, Existence et non existence de tores invariants par des difléomorphismes symplectiques [Existence and nonexistence of tori invariant under symplectic diffeomorphisms]. Séminaire sur les équations aux Dérivées Partielles 1987-1988, Exp. no. XIV. École Polytech., Palaiseau (1988) 24 (in French). [Google Scholar]
- M. Misiurewicz and K. Ziemian, Rotation sets for maps of tori. J. London Math. Soc. 40 (1989) 490–506. [Google Scholar]
- W. Stepanoff, Sur une extension du théorème ergodique. Compositio Math. 3 (1936) 239–253. [Google Scholar]
- N. Bourbaki, General Topology. [Translated from the French]. Reprint of the 1966 edition. Elements of Mathematics. Springer-Verlag, Berlin (1989) 63 (Chapters 5-10). [Google Scholar]
- L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL (1992) 268. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.
