Applications of periodic unfolding on manifolds

References

• Dobberschütz S, Böhm M. A periodic unfolding operator on certain compact Riemannian manifolds. Comptes Rendus Math. 2012;350(23–24):1027–1030.
   Web of Science ®Google Scholar
• Dobberschütz S, Böhm M. The construction of periodic unfolding operators on some Riemannian manifolds. Adv Pure Appl Math. 2014;5(1):31–45.
   Google Scholar
• Skrabalak SE, Suslick KS. Porous MoS2 synthesized by ultrasonic spray pyrolysis. J Amer Chem Soc. 2005;127:9990–9991.
   PubMed Web of Science ®Google Scholar
• Thomas JM, Thomas WJ. Principles and practice of heterogeneous catalysis. Weinheim: VCH-Wiley; 1997.
   Google Scholar
• Andersson MP, Dobberschütz S, Sand KK, et al. A microkinetic model of calcite step growth. Angewandte Chemie (Int Ed). 2016;128(37):11252–11256.
   Google Scholar
• Nielsen MR, Dobberschütz S, Sand KK, et al. The mechanisms of calcite growth inhibition deduced by microkinetic modelling of organic and inorganic inhibitors. Nat Mater. Forthcoming. 2017.
   Google Scholar
• Bensoussan A, Lions J-L, Papanicolaou G. Asymptotic analysis for periodic structures. Amsterdam: North-Holland; 1978.
   Google Scholar
• Sanchez-Palencia E. Non-homogeneous media and vibration theory. Vol. 127. Lecture notes in physics. Berlin: Springer; 1980.
   Google Scholar
• Nguetseng G. A general convergence result for a functional related to the theory of homogenization. SIAM J Math Anal. 1989;20(3):608–623.
   Web of Science ®Google Scholar
• Allaire G. Homogenization and two-scale convergence. SIAM J Math Anal. 1992;23(6):1482–1518.
   Web of Science ®Google Scholar
• Cioranescu D, Donato P. An introduction to homogenization. Oxford: Oxford University Press; 1999.
   Google Scholar
• Cioranescu D, Damlamian A, Griso G. Periodic unfolding and homogenization. Comptes Rendus de l’Académie des Sciences Paris, Series I. 2002;(335):99–104.
   Google Scholar
• Arbogast T, Douglas J, Hornung U. Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J Math Anal. 1990;21(4):823–836.
   Web of Science ®Google Scholar
• Cioranescu D, Damlamian A, Griso G. The periodic unfolding method in homogenization. SIAM J Math Anal. 2008;40(4):1585–1620.
   Web of Science ®Google Scholar
• Allaire G, Damlamian A, Hornung U. Two-scale convergence on periodic surfaces and applications. In: Bourgeat A, Carasso C, Luckhaus S, et al., editors. Mathematical modelling of flow through porous media. Singapore: World Scientific; 1995. p. 15–25.
   Google Scholar
• Cioranescu D, Donato P, Zaki R. The periodic unfolding method in perforated domains. Portugaliæ Math. 2006;63(4):467–496.
   Google Scholar
• Neuss-Radu M. Some extensions of two-scale convergence. Comptes Rendus de l’Académie des Sciences Paris, Series I. 1996;322:899–904.
   Google Scholar
• Neuss-Radu M. Mathematical modelling and multi-scale analysis of transport processes through membranes [Habilitation thesis]. University of Heidelberg. 2017.
   Google Scholar
• Peter MA. Homogenisation in domains with evolving microstructure. Comptes Rendus Mécanique. 2007;335:357–362.
   Web of Science ®Google Scholar
• van Noorden TL, Muntean A. Homogenization of a locally-periodic medium with areas of low and high diffusivity. Eur J Appl Math. 2011;22(5):493–516.
   Web of Science ®Google Scholar
• Graf I, Peter MA. A convergence result for the periodic unfolding method related to fast diffusion on manifolds. Comptes Rendus Math. 2014;352(6):485–490.
   Web of Science ®Google Scholar
• Schwarz G. Hodge decomposition - A method for solving boundary value problems. Vol. 1607. Lecture notes in mathematics. Berlin: Springer; 1995.
   Google Scholar
• Agricola I, Friedrich T. Global analysis: differential forms in analysis, geometry, and physics. Vol. 52. Graduate studies in mathematics. Providence (RI): American Mathematical Society; 2002.
   Google Scholar
• Hebey E. Sobolev spaces on Riemannian manifolds. Vol. 1635. Lecture notes in mathematics. Berlin: Springer; 1996.
   Google Scholar
• Wloka J. Partial differential equations. Cambridge: Cambridge University Press; 1992.
   Google Scholar
• Dobberschütz S. Homogenization techniques for lower dimensional structures [PhD thesis]. University of Bremen. 2012. Available from: http://nbn-resolving.de/urn:nbn:de:gbv:46-00102769-13.
   Google Scholar
• Hebey E. Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Vol. 5. Courant lecture notes in mathematics. Providence (RI): American Mathematical Society; 1999.
   Google Scholar
• Cartan H. Differential forms. Paris: Hermann; 1970.
   Google Scholar