Open Access
Issue |
ESAIM: COCV
Volume 23, Number 4, October-December 2017
|
|
---|---|---|
Page(s) | 1447 - 1471 | |
DOI | https://doi.org/10.1051/cocv/2016060 | |
Published online | 06 September 2017 |
- Z. Abdessamad, I. Kostin, G. Panasenko and V.P. Smyshlyayev, Memory effect in homogenization of a viscoelastic Kelvin–Voigt model with time-dependent coefficients. Math. Models Methods Appl. Sci. 19 (2009) 1603–1630. [CrossRef] [MathSciNet] [Google Scholar]
- E. Acerbi, V. Chiado Piat, G. Dal Maso and D. Percivale, An extension theorem from connected sets, and homogenization in general periodic domains. Nonlin. Anal. Theory Methods Appl. 18 (1992) 481–496. [Google Scholar]
- N.D. Alikakos, Lp bounds of solutions of reaction-diffusion equations. Commun. Partial Differ. Equ. 4 (1976) 827–868. [Google Scholar]
- G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992) 1482–1518. [Google Scholar]
- H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer (2010). [Google Scholar]
- P.G. Ciarlet and P. Ciarlet Jr., Another approach to linear elasticity and Korn’s inequality. C.R. Acad. Sci. Paris Ser. I 339 (2004) 307–312. [CrossRef] [MathSciNet] [Google Scholar]
- D. Cioranescu, A. Damlamian and G. Griso, The periodic unfolding method in homogenization. SIAM J. Math. Anal. 40 (2008) 1585–1620. [CrossRef] [MathSciNet] [Google Scholar]
- D. Cioranescu, A. Damlamian, P. Donato, G. Griso and R. Zaki, The periodic unfolding method in domains with holes. SIAM J. Math. Anal. 44 (2012) 718–760. [CrossRef] [MathSciNet] [Google Scholar]
- D. Cioranescu and J. Saint Jean Paulin, Homogenization of reticulated structures. Springer (1999). [Google Scholar]
- I. Diddens, B. Murphy, M. Krisch and M. Müller, Anisotropic elastic properties of cellulose measured using inelastic X-ray scattering. Macromolecules 41 (2008) 9755–9759. [CrossRef] [Google Scholar]
- H.I. Ene, M.L. Mascarenhas and J. Saint Jean Paulin, Fading memory effects in elastic-viscoelastic composites. RAIRO Model. Math. Anal. Numer. 31 (1997) 927–952. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- G.-A. Francfort and P.-M. Suquet, Homogenization and mechanical dissipation in thermoviscoelasticity. Arch. Ration. Mech. Anal. 96 (1986) 265–293. [Google Scholar]
- R.P. Gilbert, A. Panachenko and X. Xie, Homogenization of a viscoelastic matrix in linear frictional contact. Math. Methods Appl. Sci. 28 (2005) 309–328. [CrossRef] [MathSciNet] [Google Scholar]
- C.-M. Hayot, E. Forouzesh, A. Goel, A. Avramova and J.-A. Turner, Viscoelastic properties of cell walls of single living plant cells determined by dynamic nanoindentation. J. Exp. Biol. 63 (2012) 2525–2540. [Google Scholar]
- W. Jäger and U. Hornung, Diffusion, convection, adsorption, and reaction of chemicals in porous media. J. Differ. Equ. 92 (1991) 199–225. [CrossRef] [MathSciNet] [Google Scholar]
- V.V. Jikov, S.M. Kozlov and O.A. Oleinik, Homogenization of Differential Operators and Integral Functionals. Springer (1994). [Google Scholar]
- A. Korn, Über einige ungleichungen, welche in der theorie del elastichen und elektrishen schwingungen eine rolle spielen. Bulletin international de l’Académie des sciences de Cracovie, Classe des sciences mathématiques et naturelles (1909) 705–724. [Google Scholar]
- M.L. Mascarenhas, Homogenization of a viscoelastic equations with non-periodic coefficients. Proc. R. Soc. Edinb.: Sect. A Math. 106 (1987) 143–160. [CrossRef] [Google Scholar]
- F. Murat and L. Tartar, H-convergence, in Topics in the Mathematical Modelling of Composite Materials. Vol. 31 of Progr. Nonlin. Differ. Equ. Appl. Birkhäuser Boston, Boston, MA (1997) 21–43. [Google Scholar]
- J. Necas, Les méthodes directes en théorie des équations elliptiques. Academie, Prague (1967). [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. [CrossRef] [MathSciNet] [Google Scholar]
- O. Oleinik, A.S. Shamaev and G.A. Yosifian, Mathematical problems in Elasticity and Homogenization. North Holland (1992). [Google Scholar]
- A. Peaucelle, S.A. Braybrook, L. Le Guillou, E. Bron, C. Kuhlemeier and H. Hofte, Pectin-induced changes in cell wall mechanics underlie organ initiation in Arabidopsis. Curr. Biol. 21 (2011) 1720–1726. [CrossRef] [PubMed] [Google Scholar]
- S. Pelletier, J. Van Orden, S. Wolf, K. Vissenberg, J. Delacourt, Y.-A. Ndong, J. Pelloux, V. Bischoff, A. Urbain, G. Mouille, G. Lemonnier, J.-P. Renou and H. Hofte, A role for pectin de-methylesterification in a developmentally regulated growth acceleration in dark-grown Arabidopsis hypocotyls. New Phytol. 188 (2010) 726–739. [CrossRef] [PubMed] [Google Scholar]
- M. Ptashnyk, Derivation of a macroscopic model for nutrient uptake by a single branch of hairy-roots. Nonlin. Anal.: Real World Appl. 11 (2010) 4586–4596. [CrossRef] [Google Scholar]
- M. Ptashnyk, B. Seguin, Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics. ESAIM: M2AN 50 (2016) 593–631. [CrossRef] [EDP Sciences] [Google Scholar]
- E. Sanchez-Palencia, Non-Homogeneous Media and Vibration Theory. Springer (1980). [Google Scholar]
- P.J. White, The pathways of calcium movement to the xylem. J. Exp. Bot. 52 (2001) 891–899. [CrossRef] [PubMed] [Google Scholar]
- S. Wolf and S. Greiner, Growth control by cell wall pectins. Protoplasma 249 (2012) 169–175. [CrossRef] [Google Scholar]
- S. Wolf, K. Hématy and H. Höfte, Growth control and cell wall signaling in plants. Ann. Review Plant Biol. 63 (2012) 381–407. [CrossRef] [Google Scholar]
- S. Wolf, J. Mravec, S. Greiner, G. Mouille and H. Höfte, Plant cell wall homeostasis is mediated by Brassinosteroid feedback signaling. Curr. Biol. 22 (2012) 1732–1737. [CrossRef] [PubMed] [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.